Question

Factorise 2a^2+13a+20

Answer 1

Hey friend, Here is your answer-
$2 {a}^{2} + 13a + 20 = 0 \\ 2 {a}^{2} + 8a + 5a + 20 = 0 \\ 2a(a + 4) + 5(a + 4) = 0 \\ (2a + 5)(a + 4) = 0 \\ 2a + 5 = 0 \: \: \: \: \: \: \: or \: \: \: \: \: \: a + 4 = 0 \\ a = \frac{ - 5}{2} \: \: \: \: \: \: or \: \: \: \: \: \: a = - 4$
Hope it will help you.

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Answer 2

Answer:

Upon factorizing the given quadratic equation, we get the value of x to be $\frac{-5}{2} \; or -4$

Step-by-step explanation:

To factorize a quadratic equation, we try to find out 2 common factors between the second and the third term of the equation, such that these factors' sum form the 2nd term's coefficient, and the product forms the 3rd term, i.e., the constant.

Algebraically, this can be expressed as follows -

We need to find 2 constants p and q for the given quadratic equation $x^2 + ax + b = 0$ such that

$x^2 + (p+q)x + (pq) = 0\\i.e., p+q = a; \;pq = b$

Now, let us factorize the above given equation

$2a^2 + 13a + 20 = 0\\2a^2 +8a+5a+20 = 0\\2a(a+4) +5(a+4) = 0\\(2a+5) (a+4) = 0\\Thus, 2a = -5 \;or\; a = -4\\a = \frac{-5}{2} , -4$

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