Question

solve 2p^2 +19p+30=0 by factorization method
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Answer 1

Answer:

• Factorise (2p² + 19p + 30) = 0

⇒ 2p² + 19p + 30 = 0

• (15 + 4) = 19
• (15 × 4) = 60

⇒ 2p² + (15 + 4)p + 30 = 0

⇒ 2p² + 15p + 4p + 30 = 0

⇒ p(2p + 15) + 2(2p + 15) = 0

⇒ (p + 2)(2p + 15) = 0

• If we want to solve it further, either of them is 0 that's why Product is Zero

⇒ (p + 2) = 0 ⠀or, ⠀(2p + 15) = 0

⇒ p = - 2⠀ or,⠀ p = - 15/2

∴ Hence, value of p can be - 2 or - 15/2.

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How to do factorisation?

• To factorise a quadratic equation (x² + bx + c) we have to find numbers p and q such that p + q = b and pq = c.
• After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

Here is an Example :

Factorize x² + 6x + 8

To factorize x² + 6x + 8, we find two numbers p and q such that p + q = 6 and pq = 8.

Clearly, 2 + 4 = 6 and 2 × 4 = 8.

We know split the middle term 6x in the given quadratic as (2x + 4x), so that

⇢ x² + 6x + 8

⇢ x² + 2x + 4x + 8

⇢ (x² + 2x) + (4x + 8)

⇢ x(x + 2) + 4(x+ 2)

⇢ (x + 2)(x + 4)