Question

The Roots of the equation 7X²+ X-1 = 0 are
real and distinct
real and equal
not real
none of these​

Answer 1

Question:

The Roots of the equation 7x² + x - 1 = 0 are

1. Real and distinct
2. Real and equal
3. Not real
4. None of these

To find:

★ To find the nature of roots.

Answer:

★ It has Real and Distinct roots.

(Option 1)

Given:

★ An equation is given, $7 {x}^{2} + x - 1 = 0$

Step-by-step explanation:

$7 {x}^{2} + x - 1 = 0$

It's of the form, $a{x}^{2}+bx+c=0$

$Here, \: \: a = 7, \: b = 1, \: c = - 1$

We know that,

$\boxed{\Delta = {b}^{2} - 4ac}$

$\implies \Delta = {(1)}^{2} - 4 \times 7 \times - 1$

$\implies \Delta = 1 + 28 = 29$

$Now,\: \boxed{\Delta = 29 > 0}$

So, the equation will have Real and Distinct roots .

Option 1. Real and Distinct roots

More information:

The roots of the quadratic equation $a{x}^{2}+bx+c=0$ ,$a \not=0$ are found using the formula $x=\dfrac{-b ± \sqrt{{b}^{2}-4ac}}{2a}$. Here, ${b}^{2}-4ac$ called as the Discriminant ( which is denoted by ∆ ) of the quadratic equation, decides the nature of roots as follows;

∆ > 0 = Real and Unequal roots

∆ = 0 = Real and Equal roots

∆ < 0 = No Real roots

Answer 2

Answer:

Real and distinct is the answe