Question

what will be the nature of roots of quadratic equation 2x^+4x-7=0

Answer 1

Roots of given quadratic equation are real and distinct.

Given:

• A quadratic equation.
• $2 {x}^{2} + 4x - 7 = 0$

To find:

• Nature of roots.

Solution:

Concept to be used:

If a quadratic equation is given by $\bf a {x}^{2} + bx + c = 0, \: a \neq0$ ,then nature of its roots can be find by it's discriminate (D).

• $\bf D = {b}^{2} - 4ac$

1. Roots are real and distinct, if D>0
2. Roots are real and equal, if D=0
3. Roots are imaginary (no real root exists), if D<0

Step 1:

Write coefficients of x², x and constant term.

Compare the given equation with standard quadratic equation.

On comparison it is clear that

$a = 2$

$b = 4$

and

$c = - 7$

Step 2:

Find the value of D.

$D = {b}^{2} - 4ac$

or

$D = ( {4})^{2} - 4(2)( - 7)$

or

$D = 16 + 56$

or

$\bf D =72$

as

$\bf \pink{D > 0}$

Thus,

Roots of given quadratic equation are real and distinct.

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