Question

If the sum of the squares of the zeroes of the quadratic polynomial f(x)=x^2-px+70 is equal to 149, then the value of p is

Answer 1

Let α,β are the roots of the quadratic polynomial f(x) = x2+px+45 then 

 α + β = -p ---------(1) and  αβ = 45

Given  (α - β)2 = 144 

∴ (α + β)2 – 4αβ = 144

⇒ (– p)2 – 4 × 45 = 144               [Using (1)]

⇒ p 2 – 180 = 144

⇒ p 2 = 144 + 180 = 324



Thus, the value of p is ± 18.

Answer 2

Answer:

The value of p is either 17 or -17.

Step-by-step explanation:

It α and β are two zeroes of a polynomial, then the polynomial is defined as

$g(x)=x^2+(\alpha +\beta)x+\alpha \beta$           .... (1)

The given polynomial is

$f(x)=x^2-px+70$                ..... (2)

On comparing (1) and (2), we get

$\alpha +\beta=-p$

$\alpha\beta=70$

$(\alpha +\beta)^2=\alpha^2+2\alpha \beta +\beta^2$

$(-p)^2=(\alpha^2+\beta^2)+2\alpha \beta$

$(-p)^2=(149)+2(70)$

$p^2=289$

$p=\pm\sqrt{289}$

$p=\pm 17$

Therefore the value of p is either 17 or -17.