Question 1 :
Find a quadratic polynomial, the sum and product of whose zeroes are $\sqrt{2}$ and $\frac{1}{3}$, respectively.
Question 2 :
Find the zeroes of the quadratic polynomial $2x^{2} - 8x + 6$.
Question 4 :
The quadratic polynomial whose sum and product of zeros being $\sqrt{2}$ and $-\frac{3}{2}$ respectively, is:
Question 5 :
State true or false: The only value of $k$ for which the quadratic polynomial $kx^2+x+k$ has equal zeroes is $\frac{1}{2}$.
Question 6 :
If the remainder on division of $x^3+2x^2+kx+3$ by $x-3$ is 21, find the value of k.
Question 7 :
Divide the polynomial $p\left(x\right)$ by the polynomial $g\left(x\right)$ and find the quotient and remainder in the following : $p\left(x\right)$ = $x^4–3x^2+4x+5$, $g\left(x\right)$ = $x^2+1-x$
Question 8 :
Find all the zeros of $2x^4-3x^3-3x^2+6x-2$, if you know that two of its zeroes are $\sqrt{2}$ and $-\sqrt{2}$ .
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdf273b230584979a33.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 11 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $t^2–3$, $2t^4+3t^3–2t^2–9t–12$
Question 12 :
If on division of a non-zero polynomial $p\left(x\right)$ by a $g\left(x\right)$, the remainder is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$ ?
Question 13 :
Which of the following is not the graph of a quadratic polynomial?
Question 14 :
Given that $x-\sqrt{5}$ is a factor of the cubic polynomial $x^3-3\sqrt{5}x^2+13x-3\sqrt{5}$, find all the zeroes of the polynomial
Question 15 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$
Question 16 :
Given that two of the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$ are 0, the third zero is:
Question 17 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be6273b230584979a3c.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 18 :
Given that the zeroes of the cubic polynomial $x^3-6x^2+3x+10$ are of the form a, a+b, a+2b for some real numbers a and b, find the value of b.
Question 19 :
Is the statement true or false? If the zeroes of a quadratic polynomial $ax^2+bx+c$ are both negative, then, a, b and c all have the same sign.
Question 21 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be3273b230584979a38.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 22 :
For which values of a and b, are the zeroes of $q\left(x\right)=x^3+2x^2+a$ also the zeroes of the polynomial $p\left(x\right)=x^5-x^4-4x^3+3x^2+3x+b$?
Question 23 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $x^2+3x+1$, $3x^4+5x^3–7x^2+2x+2$
Question 24 :
What will the remainder be on division of $ax^2+bx+c$ by $px^3+qx^2+rx+s$, $p\ne0$ ?
Question 26 :
Find a quadratic polynomial, the sum and product of whose zeroes are 1 and 1, respectively.
Question 28 :
If the zeroes of the quadratic polynomial $x^2+\left(a+1\right)x+b$ are 2 and -3, then:
Question 29 :
Find a quadratic polynomial whose sum and product
respectively of the zeroes are as given: $-\frac{3}{2\sqrt{5}}$, $-\frac{1}{2}$
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be2273b230584979a37.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 31 :
Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.
Question 32 :
3, –1, $-\frac {1}{3}$ are the zeroes of the cubic polynomial $p\left(x\right)=3x^3-5x^2-11x-3$. Is it correct or not?
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bdf273b230584979a34.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 35 :
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be4273b230584979a3a.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 37 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a57273b230584979925.png' />
In the image above, the graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$
Question 39 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: $x^3-3x+1$, $x^5–4x^3+x^2+3x+1$
Question 41 :
Divide $3x^2 – x^3 – 3x + 5$ by $x – 1 – x^2$ and find the remainder and the quotient?
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19be3273b230584979a39.png' />
Look at the graph given above. The graph of $y=p\left(x\right)$, where $p\left(x\right)$ is a polynomial. Here, find the number of zeroes of $p\left(x\right)$.
Question 45 :
State true or false: If all three zeroes of a cubic polynomial $x^3+ax^2-bx+c$ are positive, then at least one of a, b and c is non-negative.
Question 46 :
Find the zeroes of the quadratic polynomial using the given sum and product respectively of the zeroes: $\frac{21}{8}$, $\frac{5}{16}$
Question 47 :
State true or false: If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial.
Question 48 :
The zeroes of the polynomial $x^4-6x^3-26x^2-138x-35$ are $2\pm \sqrt {3}$, 7, -5.
Question 49 :
State true or false: If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Question 50 :
If the polynomial $x^4-6x^3+16x^2-25x+10$ is divided by another polynomial $x^2– 2x+k$, the remainder comes out to be x + a, then k and a are 5 and -5 respectively.
