Question

Nature of the roots of an equation 3x^2+7x+8​

Answer 1

Answer:

3x2 – 7x + 8 = 0. Here a = 3, b = –7, c = 8 ∴ D = b2 – 4ac = (–7)2 – 4 x 3 x 8 = 49 – 96 = –47 ∵ D < 0 ∴ Roots are not real.

Answer 2

Roots of equation $\bf 3 {x}^{2} + 7x + 8$ are not real.

Given:

• A quadratic equation.
• $3 {x}^{2} + 7x + 8$

To find:

• Find nature of roots of given quadratic equation.

Solution:

Formula\Concept to be used:

Standard quadratic equation is written as

$\bf a {x}^{2} + bx + c, \: where \: a \neq0$

Nature of roots depends upon Discriminant.

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

1. if D= 0; Roots are real and equal.
2. if D> 0; Roots are real and distinct.
3. if D< 0; Roots are not real (Imaginary)

Step 1:

Compare the given quadratic equation with standard equation and write the coefficients.

here

$a = 3$

$b = 7$

and

$c = 8$

Step 2:

Find the value of discriminant.

$D = 49 - 4 \times 3 \times 8$

or

$D = 49 - 96$

or

$\bf D = - 47$

Step 3:

Write the conclusion on nature of roots.

It is clear that D= -47

So,

D<0; Roots of equation are not real.

or we can say roots are Imaginary.

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