Question

If one of the zeroes of the quadratic polynomial x^2+ bx +c is negative of the other, then:
(a) c is positive and b=0 (b) c is negative and b=0 (c) b≠ 0 and c is positive (d) b≠0 and c is negative

please choose the correct answer and explain why.... best answer would be marked the brainliest

Answer 1

Answer:

b) c is negative and b=0

Step-by-step explanation:

The given polynomial is

${x}^{2} + bx + c$

If α, β are the zeroes of the polynomial, they satisfy the equation

${x}^{2} + bx + c = 0$

Hence

$\alpha + \beta = - b \: and \: \alpha \beta = c$

It is given that

$\alpha = - \beta$

So

$b = - ( \alpha + \beta ) = - ( - \beta + \beta )$

$or \: b = 0$

and

$c = \alpha \beta = - { \beta }^{2} \leqslant 0$

The correct option is b) c is negative and b=0

Answer 2

THE ANSWER IS IN THE ABOVE IMAGE ☝️☝️☝️