Question

2) Find the value of discriminant and decide nature of roots.
x² + 2x - 9=0. ​

Answer 1

Answer:

discriminant= 40

Step-by-step explanation:

the nature of the roots is given below

it will be two distinct real irrational number

Answer 2

ANSWER:

2 distinct roots

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EXPLANATION:

Here this is a question from quadratic equation, where we have to find the nature of the roots as well as value of discriminant of the given quadratic equation.

To find the nature of roots we have to first find the value of D and nature of roots can be expressed as follows:

$\boxed{\begin{array}{|c|| c|}\cline{1-2}\bf{Discriminant}&\bf{Nature}\\\cline{1-2}\sf{-ve}&\sf{No\:real\:roots}\\\cline{1-2} \sf{+ve}&\sf{Two\:distinct\:roots}\\\cline{1-2}\sf{0}&\sf{Two\:equal\:roots}\\\cline{1-2}\end{array}}$

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So let's start!

Given quadratic equation:

X²+2x-9=0

Here value of:

→ Coefficient of x², a=1

→ Coefficient of x, b=2

→ Constant term, c=-9

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We have formula of Discriminant:

★D=b²-4ac

D=(2)²-4(1)(-9)

D=4+36

D=40

Here value of D comes out to be +ve.So there are 2 distinct real roots in the given quadratic equation.

Please note that here D refers to Discriminant.

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ADDITIONAL INFORMATION:

Quadratic formula:

-It is a formula to find value of roots of the quadratic equation when middle term can't be splitted into the factors.

It is expressed as:

$\sf{x=\dfrac{-b\pm\sqrt{D}}{2a}}$

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