Solve the following by formula method:-
( i ) x^2-3x-10=0
( ii ) 2x^2+x-6=0
Answers
Answer:
(i)
Step-by-step explanation:
The roots of the polynomial are the same as the zeros of the polynomial.
Therefore, roots can be found by factorizing the quadratic equation into two linear factors and after that equating each factor to zero.
(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 and x + 2 = 0
x = 5 and x = - 2
Therefore, roots are : - 2, 5
(ii) 2x2 + x - 6 = 0
2x2 + 4x - 3x - 6 = 0
2x (x + 2) - 3 (x + 2) = 0
(2x - 3) (x + 2) = 0
2x - 3 = 0 and x + 2 = 0
2x = 3 and x = - 2
x = 3/2 and x = - 2
Therefore, roots are: 3/2, -2
(iii) √2x2 + 7x + 5√2 = 0
√2x2 + 5x + 2x + 5√2 = 0
√2x2 + 2x + 5x + 5√2 = 0
(√2x + 5) (x + √2) = 0
√2x + 5 = 0 or x + √2 = 0
√2x = - 5 or x = - √2
x = - 5/√2 or x = - √2
Therefore, roots are: - 5/√2, - √2
(iv) 2x2 - x + 1/ 8 = 0
Multiplying both sides of the equation by 8:
2(8) x2 - 8(x) + (8)(1/ 8) = (0)8
16x2 - 8x + 1 = 0
16x2 - 4x - 4x + 1 = 0
4x (4x - 1) -1 (4x - 1) = 0
(4x - 1) (4x - 1) = 0
(4x - 1)2 = 0
4x - 1 = 0
x = 1/4 and x = 1/4
Roots are: 1/4, 1/4
(v) 100x2 - 20x + 1 = 0
100x2 - 20x + 1 = 0
100x2 - 10x - 10x + 1 = 0
10x(10x - 1) -1(10 x - 1) = 0
(10x - 1)(10 x - 1) = 0
(10x - 1)2 = 0
10x - 1 = 0
x =1/10 and x = 1/10
Roots are: 1/10, 1/10