Question

The roots of the equation 7x^2 +x-1=0 are:

real and distinct
real and equal
not real
none of these​

Answer 1

Correct option: First one -> real and distinct.

Explanation:

To evaluate the roots of the equation 7x^2 + x - 1 = 0, lets find the discriminant Delta using the Bhaskara's formula:

`\Delta = b^(2) - 4ac`

Where a, b and c are coefficients of the quadratic equation (in this case, a = 7, b = 1 and c = -1)

So we have that:

`\Delta = 1^(2) - 4*7*(-1) = 29`

To evaluate the roots of the equation, we have the following cases:

`\Delta > 0` : Two roots real and distinct

`\Delta = 0` : Two roots real and equal

`\Delta < 0` : Two roots not real

In our case, we have
`\Delta > 0`, so the roots are real and distinct.

Correct option: First one