Question

if -1 and 3 are the roots of x2+p x+q=0.find the value of p and q​

Answer 1

Your Answer:

Given:-

• -1 and 3 are the roots of $\tt x^2+p x+q=0$

To find:-

• Values of p and q

Solution:-

We know

$\tt \alpha + \beta= \dfrac{-b}{a}\\\\ and \\\\ \tt \alpha \beta = \dfrac{c}{a}$

where alpha and beta are the zeroes

• alpha = -1

• beta = 3

So, putting values of alpha and beta in the above equations

we get,

$\tt \alpha + \beta = \dfrac{-b}{a} \\\\ \tt \Rightarrow -1 + 3 = -p \\\\ \Rightarrow 2=-p \\\\ \Rightarrow -2=p$

and

$\tt \alpha \beta=\dfrac{c}{a} \\\\\tt \Rightarrow (-1)(3)=q \\\\\tt \Rightarrow -3=q$

We have p = -2 and q= -3