Question

A polynomial p(x) is given as 2x^2-3kx+5
One of the zeros of p(x) is -1
Find k.

Answer 1

`k = -(7)/(3)`

Explanation:

Given :

p(x) = 2x² − 3kx + 5

Since, -1 is a zero for p then :

p(-1) = 0

Solving the equation p(-1) = 0 for k :

p(-1) = 0

⇔ 2(-1)² − 3k(-1) + 5 = 0

⇔ 2 + 3k + 5 = 0

⇔ 3k = -5 - 2

⇔ 3k = -7

⇔ k = -7/3

NOTE :

If -1 is a zero of p

`\Longrightarrow k = -(7)/(3)`

`\Longrightarrow p(x) = 2x^2 - 3((-7)/(3)) x + 5\\\Longrightarrow p(x) = 2x^2+ 7x + 5`