Question 2 :
Check whether the following is quadratic equation : $x^2 + 3x + 1 = (x-2)^2$
Question 3 :
Check whether the following is a quadratic equation: $(x – 2)(x + 1) = (x – 1)(x + 3)$
Question 4 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is
Question 7 :
Find the roots of the quadratic equation (by using the quadratic formula): $-x^2+7x-10=0$
Question 8 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 + x + 4 = 0$
Question 9 :
Represent the following situation in the form of a quadratic equation : The product of two consecutive positive integers is 306. We need to find the integers.
Question 10 :
Represent the following situation in the form of quadratic equations: The product of two consecutive positive integers is 306. We need to find the integers.
Question 11 :
Find the roots of the following quadratic equation (by the factorisation method): $\frac{2}{5}x^2-x-\frac{3}{5}=0$
Question 13 :
State True or False: Every quadratic equation has at least one real root.
Question 14 :
Justify why the following quadratic equation has two distinct real roots: $\left(x-1\right)\left(x+2\right)+2=0$
Question 15 :
Find the roots of the following quadratic equation by factorisation: $100x^2 – 20x + 1 = 0$
Question 16 :
Find the roots of the quadratic equation (by using the quadratic formula): $5x^2+13x+8=0$
Question 17 :
State True or False: If the coefficient of $x^2$ and the constant term have the same sign and if the coefficient of $x$ term is zero, then the quadratic equation has no real roots.
Question 18 :
Does the following equation has the sum of its roots as 3? $-x^2+3x-3=0$
Question 19 :
Justify why the following quadratic equation has no two distinct real roots: $\left(x+4\right)^2-8x=0$
Question 24 :
Find the values of k for each of the following quadratic equations, so that they have two equal roots: $2x^2 + kx + 3 = 0$
Question 25 :
Check whether the following is a quadratic equation: $(x + 1)^2 = 2(x – 3)$
Question 26 :
Check whether the following is quadratic equation : $x^2 - 2x = (-2)(3-x)$
Question 27 :
Justify why the following quadratic equation has two distinct real roots: $3x^2-4x+1=0$
Question 28 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.
Question 29 :
Find the roots of the following quadratic equation: $3x^2 – 4\sqrt{3}x + 4 = 0$.
Question 31 :
State True or False whether the following quadratic equation has two distinct real roots: $x\left(1-x\right)-2=0$
Question 33 :
Find the roots of the following quadratic equation (by the factorisation method): $2x^2+\frac{5}{3}x-2=0$
Question 35 :
Find the roots of the quadratic equation (by using the quadratic formula): $x^2-3\sqrt{5}x+10=0$
Question 36 :
Using method of completing the square , $x^2+4x$ can be written as ?
Question 37 :
Does the following equation has the sum of its roots as 3? $\sqrt{2}x^2-\frac{3}{\sqrt{2}}x+1=0$
Question 38 :
A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is?
Question 39 :
Find the roots of the quadratic equations, if they exist, by applying quadratic formula: $2x^2 – 7x + 3 = 0$
Question 41 :
Which constant must be added and subtracted to solve the quadratic equation $9x^2+\frac{3}{4}x-\sqrt{2}=0$ by the method of completing the square?
Question 42 :
Find the roots of the following quadratic equation by factorisation: $\sqrt{2}x^2+7x+5\sqrt{2}=0$
Question 43 :
Using method of completing the square , solve for x: $4x^2+3x+5=0$
Question 45 :
State True or False: Every quadratic equation has at most two roots.
Question 46 :
Find the nature of the roots of the quadratic equation $2x^2 – 4x + 3 = 0$.
Question 47 :
Check whether the following is a quadratic equation: $(x + 2)^3 = 2x (x^2 – 1)$
Question 49 :
Check whether the following is a quadratic equation: $(x + 2)^3 = x^3 – 4$
Question 50 :
Justify why the following quadratic equation has two distinct real roots: $\left(x+1\right)\left(x-2\right)+x=0$
