Question

Find the zeroes of the quadratic polynomial ax2 + (a + b)x + b.
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Answer 1

p(x) = ax² + (a + b)x + b

☛ p(x) = ax² + ax + bx + b

☛ p(x) = ax( x + 1) + b(x + 1)

☛ p(x) = (x + 1)(ax + b)

x + 1 = 0 or ax + b = 0

x = -1 or x = -b/a

Hence, zeroes of p(x) are -1 and -b/a

Answer 2

The zeroes of p(x) are $-1$ and $-\frac{b}{a}$.

Given:

the quadratic polynomial $ax^{2} +(a+b)x+b$.

To find:

We have to find the zeroes of the quadratic polynomial  $ax^{2} +(a+b)x+b$.

Solution:

This is a simple problem for quadratic polynomials.

Let us tackle this problem.

We can easily solve this problem as follows.

Let,

p(x) = ax² + (a + b)x + b

⇒ p(x) = ax² + ax + bx + b

⇒ p(x) = ax( x + 1) + b(x + 1)

⇒ p(x) = (x + 1)(ax + b)

Therefore,

x + 1 = 0    or    ax + b = 0

⇒x = -1      or     x = $-\frac{b}{a}$

Hence, the zeroes of p(x) are $-1$ and $-\frac{b}{a}$.

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