Question

If x+a is factor of 2x^2+2ax+5x+10 find a

Answer 1

Step-by-step explanation:

Consider the given polynomial to be represented by p(x)

p(x)=2x²+2ax+5x+10

Given that x+a is a factor of the polynomial.

Note,

If y+m is a factor of a polynomial,then the value of y would be a zero of the polynomial

Thus,-a would be a zero of the above polynomial

Implies,

p(x)=p(-a)=0

Now,

p(-a)=2(-a)²+2a(-a)+5(-a)+10

→0=2a²-2a²-5a+10

→10-5a=0

→5a=10

→a=2

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•The polynomial would be:-

p(x)=2x²+4x+5x+10

=2x²+9x+10

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

$\boxed{\bf{a = 2}}$

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Given :- (x + a) is a factor of p(x) = 2x² + 2ax + 5x + 10

To find :- Value of a

Solution :-

Given that (x + a) is a factor of p(x) = 2x² + 2ax + 5x + 10

Now find zero of (x + a)

To find zero equate x + a to 0

x + a = 0

x = - a

Therefore by factor theorem p(-a) = 0

p(- a) = 0

p(x) = 2x² + 2ax + 5x + 10

So, p(- a) = 2(-a)² + 2(a)(- a) + 5(-a) + 10

Now, Substitute x = - a in p(x)

2(-a)² + 2a(-a) + 5(-a) + 10 = 0

2a² - 2a² - 5a + 10 = 0

- 5a + 10 = 0

- 5a = - 10

5a = 10

a = 2

$\boxed{\bf{a = 2}}$

$\mathfrak{\large{\underline{\underline{Extra\:info:-}}}}$

What is factor theorem ?

If (x - a) is a factor of the polynomial p(x), then p(a) = 0. Also p(a) = 0, then (x - a) is a factor of p(x)

What is a polynomial ?

An algebraic expression in which the variables involved have only negative integral powers is called a polynomial.

• If the variable of a polynomial is x, we may denote the polynomial P(x) q(x) are r(x).

Example :-

p(x) = 3x² + 2x + 8

q(z) = 4z² + 5z - 1