Question

Solve the following equations by the method of factorization:
1. 7x^2 + 49 = 0
2. 2x^2 +1 = 0​

Answer 1

Answer:

7x+1

Step-by-step explanation:

1) To find the factor of the (1+7x)² + (49x²-1) we will solve the terms individually.

2) (1+7x)² + (49x²-1)

(1+7x)² + (7x+1)(7x-1)   { By the Identity A²-B²= (A+B)(A-B) }(7x+1)(1+7x+7x-1)   { taking out the common terms}(7x+1)(14x)

3) The factors of the (1+7x)² + (49x²-1) are 7x+1 and 14x.

(7x+1) and 14x are factors.

The equation : x2+7x−1=0 is of the form ax2+bx+c=0 where:

a=1,b=7,c=−1

The Discriminant is given by:

Δ=b2−4⋅a⋅c

=(7)2−(4⋅(1)⋅−1)

=49+4=53

The solutions are found using the formula

x=−b±√Δ2⋅a

x=−7±√532⋅1=−7±√532