Question

if alpha and beta are the zeroes of quadratic polynomial p(x)=x square -7x+k such that alpha square +beta square=29 find the value of k​

Answer 1

Step-by-step explanation:

x^2-7x+k ________(i)

On comparing the above equation with ax^2+bx+c=0, we get

a=1, b= -7 and c=k

since, alpha+beta=-b/a

= 7/1

= 7

Also, alpha×beta= c/a

= k/1

= k

We know that (a+b)^2= a^2+b^2+2ab

therefore, (alpha+beta)^2= alpha^2+beta^2+2alpha×beta

(7)^2= 29+2×k

49-29= 2k

20/2= k

k= 10