Question

If two zeroes of the cubic polynomial p(x) = ax³ + bx² + cx+d are 0, then c = d = 0. state true or false.justify your statement.​

Answer 1

Answer:

True

Step-by-step explanation:

explanation in image pinned.

Answer 2

Step-by-step explanation:

Given:

$p(x) = a {x}^{3} + b {x}^{2} + cx + d$

if two zeros of cubic polynomial are 0,then c=d=0.

To find: State true and false with Justification.

Solution:

The statement is true.

Justification:

Let $\alpha,\beta$ and $\gamma$

are the zeros of cubic polynomial,then relationship between zeros and coefficient of x³,x²,x and constant term is given by

$\alpha + \beta + \gamma = \frac{ - b}{a}...eq1 \\ \\ \alpha \beta + \beta \gamma + \alpha \gamma = \frac{c}{a}...eq2 \\ \\ \alpha \beta \gamma = \frac{ - d}{a}...eq3$

ATQ, two zeros are zero.

Let say,

$\bold{\green{\alpha = 0}} \\ \bold{\orange{ \beta = 0}}$

put these values of $\alpha,\beta$ in eq2 and eq3

$\alpha \beta + \beta \gamma + \alpha \gamma = \frac{c}{a} \\ \\ (0)(0) + (0) \gamma + (0) \gamma = \frac{c}{a} \\ \\ \frac{c}{a} = 0 \\ \\ or \\ \\\bold{\red{ c = 0}}$

and

$\alpha \beta \gamma = \frac{ - d}{a} \\ \\ (0)(0) \gamma = \frac{ - d}{a} \\ \\ \frac{ - d}{a} = 0 \\ \\ - d = 0 \\ \\ or \\ \\ \bold{\red{d = 0}}$

Therefore it is true that if two zeros of cubic polynomial are 0,then c=d=0.

Final answer:

True

Hope it helps you.

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