Find the constant $a$ such that\[(x^2 - 3x + 4)(2x^2 +ax + 7) = 2x^4 -11x^3 +30x^2 -41x +28.\]

Mathematics

1 answer:

Colt1911 [192]3 years ago

4 0

The value of constant a is -5

Further explanation:

We will use the comparison of co-efficient method for finding the value of a

So,

Given

$(x^2 - 3x + 4)(2x^2 +ax + 7)\\= x^2((2x^2 +ax + 7)-3x((2x^2 +ax + 7)+4(2x^2 +ax + 7)\\= 2x^4+ax^3+7x^2-6x^3-3ax^2-21x+8x^2+4ax+28\\Combining\ alike\ terms\\=2x^4+ax^3-6x^3+7x^2-3ax^2+8x^2-21x+4ax+28\\= 2x^4 +(a-6)x^3+(15-3a)x^2-(21-4a)x+28\\$

As it is given that

(x^2 - 3x + 4)(2x^2 +ax + 7) = 2x^4 -11x^3 +30x^2 -41x +28

In this case, co-efficient of variables will be equal, so we can compare the coefficients of x^3, x^2 or x

Comparing coefficient of x^3

$a-6 = -11\\a = -11+6\\a = -5$

So the value of constant a is -5

Keywords: Polynomials, factorization

Learn more about factorization at:

#LearnwithBrainly

You might be interested in

Evaluate<br>THANK YOU!!!

cestrela7 [59]

Answer:

Step-by-step explanation:

Work is shown in the picture below. I split the work of solving the numerator and denominator apart so it's easier to understand.

The most confusing part may be solving the $\frac{2}{\frac{1}{3} }$ . However, it's basically asking you to divide 2 by $\frac{1}{3}$ . Remember that in order to divide something in fraction form, you the "flip" the numerator and denominator of the divisor, meaning the numerator now becomes the denominator and the denominator now becomes the numerator. This results in $\frac{2}{1}$ · $\frac{3}{1}$ part - notice how the $\frac{1}{3}$ was flipped to $\frac{3}{1}$ .