## Quadratic Equations Test 1

Instructions

For the following questions answer them individually

Q 1

Find a?

A) Two quadratic equations $$x^2-ax+20=0$$ and $$x^2-8x+b=0$$ have roots that are natural numbers

B) a+b=16

Q 2

For how many values of p are the roots of the equation $$(x-p)^{2} + x^{2} = 2$$ are equal and negative?

Q 3

The value of $$\frac{(1-d^3)}{(1-d)}$$ is

Q 4

What are the values of p for which the roots 'a' and 'b' of the equation $$x^{2} +4x + 2p-2$$=0 satisfy the inequality $$\frac{a}{b}$$+$$\frac{b}{a} < 2$$ ?

Q 5

Let p and q be the roots of the quadratic equation $$x^2 - (\alpha - 2) x - \alpha -1= 0$$ . What is the minimum possible value of $$p^2 + q^2$$?