Question 1 :
Find the roots of the following quadratic equation by factorisation: $2x^2 + x – 6 = 0$

Question 2 :
If $\frac{1}{2}$ is a root of the equation $x^2+kx-\frac{5}{4}=0$, then the value of k is?

Question 3 :
Find the nature of the roots of the equation $3x^2 – 2x +\frac{1}{3} = 0$.

Question 5 :
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 6 :
Check whether the following is a quadratic equation: $x^2 – 2x = (–2) (3 – x)$

Question 7 :
Check whether the following is quadratic equation : (2x- 1)(x -3)=(x +5)(x -1)

Question 8 :
Find the roots of the following quadratic equation (by the factorisation method): $3x^2+5\sqrt{5}x-10=0$

Question 9 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b61273b23058497998e.png' /> In the centre of a rectangular lawn of dimensions $50m×40m$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 $m^2$ in the above figure. Find the breadth of the pond.

Question 10 :
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.