Factorize- 5 -5 x2 - 20 x - 3 -5

5 √(5) x^2 + 20 x + 3 √(5) = 5 √(5)x^2 + 5x + 15 x + 3 √(5) ∵ 5 √(5)× 3 √(5) = 75 ∴ 75 = 15 × 5 20 = 15+5 = √(5)x ( 5x + √(5)) + 3 (5x + √(5)) = (5x+ √( ...

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Byju's Answer

Standard IX

Mathematics

Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorize: 5 ...

Question

Factorize:

$5 \sqrt{5} x^{2} + 20 x + 3 \sqrt{5}$

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Solution

$5 \sqrt{5} x^{2} + 20 x + 3 \sqrt{5} = 5 \sqrt{5} x^{2} + 5 x + 15 x + 3 \sqrt{5} ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} ∵ 5 \sqrt{5} \times 3 \sqrt{5} = 75 ∴ 75 = 15 \times 5 20 = 15 + 5 \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭ = \sqrt{5} x (5 x + \sqrt{5}) + 3 (5 x + \sqrt{5}) = (5 x + \sqrt{5}) (\sqrt{5} x + 3)$

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Q. Solve:

5 \sqrt{5} x^{2} + 20 x + 3 \sqrt{5} = 0

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Factorize: 5√5x2+20x+3√5

5√5x2+20x+3√5=5√5x2+5x+15x+3√5⎧⎪⎨⎪⎩∵5√5×3√5=75∴75=15×520=15+5⎫⎪⎬⎪⎭=√5x(5x+√5)+3(5x+√5)=(5x+√5)(√5x+3)

Factorize:

$5 \sqrt{5} x^{2} + 20 x + 3 \sqrt{5}$