Question

1. Find the value of k in each of the following quadratic equations, for which the
given value of x is a root of the given quadratic equation.
(a) 3x2 - kx - 2 = 0, x = 2
(b) 14x² - 27x + k = 0; x = 5/2​

Answer 1

Step-by-step explanation:

this is the first one

Answer 2

(A) using remainder theorem

p(x)=3x^2 - kx - 2 = Remainder

when we use 2 instead of x in this polynomial it should give 0 as it is the zero of the p(x) so..

p(2)=3(2)^2 -k(2)-2=0

12-2k-2=0

10=2k

5=k

(B) using remainder theorem

p(x)=14x² - 27x + k= Remainder

when we use 5/2 instead of x in this polynomial it should give 0 as it is the zero of the p(x) so..

p(2)=14(5/2)^2 -27(5/2)+k=0

175/2-135/2+k=0

20+k=0

k=-20