Question

if the square of the difference of the quadratic polynomial f(x) = x square + px +45 is equal to 144 ,find the value of p .​

Answer 1

Answer:

Let the quadratic equation

${x}^{2} + px + 45 = 0$

Let the roots are, a and b.

So,

As per question

(a-b)^2= 144

${a}^{2} + {b}^{2} - 2ab \: = 144$

Or,

$( {a + b})^{2} - 4ab = 144$

So,

${p}^{2} - 4 \times 45 = 144$

${p}^{2} = 324$

So,

$p \: = + 18 \: or \: - 18$