Question

Solve these quadratic equations and find the roots.
1. x²-5x-14-0
2. X² = 11x -28
3. 6x- X = 5
4. 12x = 25x
please as fast as possible​

Answer 1

Step-by-step explanation:

Find the roots of the following quadratic equations by factorization:

(i) x2 – 3x – 10 = 0

(ii) 2x2 + x – 6 = 0

(iii) √2 x2 + 7x + 5√2 = 0

(iv) 2x2 – x + 1/8 = 0

(v) 100x2 – 20x + 1 = 0

Answer

(i) x2 – 3x – 10=0

x2 - 5x + 2x – 10=0

x(x - 5) + 2(x - 5)=0

(x - 5)(x + 2)=0

∴ x - 5 = 0 or x + 2 = 0

x = 5 or x = -2

(ii) 2x2 + x – 6=0

2x2 + 4x - 3x – 6=0

2x(x + 2) - 3(x + 2)=0

(x + 2)(2x - 3)=0

∴ x + 2 = 0 or 2x - 3 = 0

x = -2 or x = 3/2

(iii) √2 x2 + 7x + 5√2=0

√2 x2 + 5x + 2x + 5√2 =0

x (√2x + 5) + √2(√2x + 5)=0

(√2x + 5)(x + √2)=0

∴ √2x + 5 = 0 or x + √2 = 0

x = -5/√2 or x = -√2

(iv) 2x2 – x + 1/8=0

1/8 (16x2 - 8x + 1)=0

1/8 (16x2 - 4x -4x + 1)=0

1/8 (4x(4x - 1) -1(4x - 1))=0

1/8(4x - 1)2 = 0

(4x - 1) = 0 or (4x - 1) = 0

x = 1/4 or x = 1/4

(v) 100x2 – 20x + 1=0

100x2 – 10x - 10x + 1=0

10x(10x - 1) -1(10x - 1)=0

(10x - 1)2 =0

∴ (10x - 1) = 0 or (10x - 1) = 0

x = 1/10 or x = 1/10