Question

Quadratic equation
Class 10th (CBSE)
Solve it neatly
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Answer 1

Answer:

I used product sum method to find factors.

It won't affect your marks in anyway.

Answer 2

EXPLANATION.

Roots of the quadratic equations,

(1) = x² - 3x - 10 = 0.

Factorizes into middle term split, we get.

⇒ x² - 5x + 2x - 10 = 0.

⇒ x(x - 5) + 2(x - 5) = 0.

⇒ (x + 2)(x - 5) = 0.

⇒ x = -2  and  x = 5.

(2) = 2x² + x - 6 = 0.

Factorizes into middle term split, we get.

⇒ 2x² + 4x - 3x - 6 = 0.

⇒ 2x(x + 2) -3(x + 2) = 0.

⇒ (2x - 3)(x + 2) = 0.

⇒ x = 3/2  and  x = -2.

(3) = √2x² + 7x + 5√2 = 0.

Factorizes into middle term splits, we get.

⇒ √2x² + 5x + 2x + 5√2 = 0.

⇒ x(√2x + 5) +√2(√2x + 5) = 0.

⇒ (x + √2)(√2x + 5) = 0.

⇒ x = -√2  and  x = -5/√2.

(4) = 2x² - x + 1/8 = 0.

Take L.C.M in this equation we get.

⇒ 16x² - 8x + 1 = 0.

Factorizes into middle term splits, we get.

⇒ 16x² - 4x - 4x + 1 = 0.

⇒ 4x(4x - 1) - 1( 4x - 1) = 0.

⇒ (4x - 1)(4x - 1) = 0.

⇒ (4x - 1)² = 0.

⇒ x = 1/4.

(5) = 100x² - 20x + 1 = 0.

Factorizes into middle term splits, we get.

⇒ 100x² - 10x - 10x + 1 = 0.

⇒ 10x(10x - 1) - 1(10x - 1) = 0.

⇒ (10x - 1)(10x - 1) = 0.

⇒ (10x - 1)² = 0.

⇒ x = 1/10.