Question 1 :
Does the following equation has the sum of its roots as 3? $-x^2+3x-3=0$
Question 2 :
Using method of completing the square , $9x^2-15x+6=0$ can be written as ?
Question 3 :
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 4 :
Values of $k$ for which the quadratic equation $2x^2–kx+k=0$ has equal roots is
Question 5 :
Check whether the following is quadratic equation : $x^2 + 3x + 1 = (x-2)^2$
Question 6 :
What are the roots of $6x^2-\sqrt{2}x-2=0$ (by the factorisation of the corresponding quadratic polynomial)?
Question 7 :
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present age of Nisha.
Question 8 :
Check whether the following is a quadratic equation: $(x + 2)^3 = x^3 – 4$
Question 9 :
Find the roots of the following quadratic equation: $2x^2 – 6x + 3 = 0$.
Question 10 :
A quadratic equation $ax^2 + bx + c =0$ has no real roots when :
Question 12 :
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 13 :
Check whether the following is quadratic equation : $x^2 - 2x = (-2)(3-x)$
Question 14 :
At $t$ minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than $\frac{t^2}{4}$ minutes. Find $t$.
Question 15 :
State True or False: If in a quadratic equation, the coefficient of x is zero, then the quadratic equation has no real roots.
