Question

Find the nature of the roots of the quadratic equation 2 x square - 4 x + 3 is equal to use zero using its discriminant

Answer 1

Answer:

The roots of the given quadratic equation are imaginary.

Step-by-step explanation:

If a quadratic equation is,

$ax^2+bx+c$

Then,

$D=b^2-4ac$ is called the discriminant of the quadratic equation,

If D > 0, then, the quadratic equation has two distinct real roots,

If D < 0, then, the quadratic equation has two distinct imaginary roots,

If D = 0, then, the quadratic equation has two real equal roots,

Here, the given quadratic equation is,

$2x^2-4x+3$

Since, (4)² - 4×2×3 = 16 - 24 = -8 < 0,

Hence, both roots of the given equation are imaginary.

Answer 2

Answer:

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10th

Maths

Quadratic Equations

Nature of Roots

Discuss the nature of roots...

MATHS

Discuss the nature of roots of the given equation: x2+3x−4=0

December 26, 2019Manju Chandar

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ANSWER

We know that while finding the root of a quadratic equation ax2+bx+c=0 by quadratic formula x=2a−b±b2−4ac, 

if b2−4ac>0, then the roots are real and distinct 

if b2−4ac=0, then the roots are real and equal and

if b2−4ac<0, then the roots are imaginary.

Here, the given quadratic equation x2+3x−4=0 is in the form ax2+bx+c=0where a=1,b=3 and c=−4, therefore,

  

b2−4ac=(3)2−(4×1×−4)=9+16=25>0

Since b2−4ac>0   

Hence the roots are real and distinct.