Question

if alpha + beta are zeroes of the polynomial p(x)=x^2+6x+k . Find the value of k such that alpha square + beta square = 40.

Answer 1

EXPLANATION.

• GIVEN

a and b are zeroes of the polynomial

p(x) = x^2 + 6x + k

• GIVEN

a^2 + b^2 = 40

TO FIND VALUE OF K.

equation = x^2 + 6x + k

sum of zeroes = a + b = -b/a = -6

products of zeroes = ab = c/a = k

a^2 + b^2 = 40

FORMULA OF A^2 + B^2

a^2 + b^2 = ( a + b)^2 - 2ab

put the value in above equation

we get,

( -6)^2 - 2(k) = 40

36 - 2k = 40

-2k = 4

k = - 2

Hence,

value of k = -2