Question

What is the nature of roots of quadratic equation 4x2+2x-3=0

Answer 1

D=b²-4ac

=2²-4*4*-3

=4+48

=52

since d>0, roots are real

Answer 2

Answer:

The nature of the roots of the given quadratic equation is real and distinct .

Step-by-step explanation:

A quadratic equation is an equation of the form $ax^{2} +bx+c=0$ where $a\neq 0$ . Since it contains the term of $x^{2}$ , $x$ has two values.

These  values can be found in three methods

1. Using quadratic formula
2. By the method of factorization
3. Completing the square method.

In this question we are asked to find the nature of roots, not the values.

Nature of roots are determined by calculating the discriminant $b^{2} -4ac$ .

Here $a=4,\ b=2,\ c=-3$

Therefore $b^{2} -4ac=2^{2} -4(4)(-3)$

                               [tex]=4+48\\ \\ =52[/tex]

Since $b^{2} -4ac>0$ ,

this equation has real and distinct roots.

That is nature of the roots are real and distinct.

thank you