Question

decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring. −b b2 − 4ac 2a use the part of the quadratic formula that you chose above and find its value, given the following quadratic equation: 2x2 7x 3 = 0

Answer 1

If b^2 - 4ac is a perfect square, then the equation can be solved by factoring.

2x^2 + 7x + 3 = 0

a = 2, b = 7, c = 3

b^2 - 4ac = 7^2 - (4 x 2 x 3) = 49 - 24 = 25

Answer 2

Explanation:

A quadratic equation can be factorised if and only if there are rational roots.

For any quadratic equation the discriminant decides about the nature of roots.

Thus only if the discriminant is a perfect square we can have rational roots and in this case only factorization is possible.

In the given equation

`2x^2+ 7x+ 3 = 0\\a=2, b=7, c=3\\b^2-4ac = 1`

Since 1 is a perfect square we can factor and solve

`2x^2 +7x +3 = 0\\(2x+1)(x+3)=0\\x=-1/2 or x = -3`