Question

TRUE OR FALSE

All quadratic equations whose discriminatn is none negative have two rational roots?____

Answer 1

All quadratic equations whose discriminant is nonnegative have two rational roots is FALSE

Quadratic equation:

• It is of the form ax²+bx+c=0  where a  , b and c are real also  a≠0.

Discriminant

• D =  b²-4ac is called discriminant.
• D >0 roots are real and distinct
• D =0 roots are real and equal
• D < 0 roots are imaginary ( not real ) and different

Understanding with example

Assume a Quadratic Equation x² - 4x  +  1 = 0

Comparing with ax²+bx+c=0

a = 1

b = -4

c = 1

D = b²-4ac

=> D = (-4)² - 4(1)(1)  = 12

Discriminant is non negative

Roots of Quadratic Equation are given by:

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

Substituting b= -4 , D = 12 , a = 1

$\dfrac{4\pm\sqrt{12} }{2(1)} =\dfrac{4\pm2\sqrt{3} }{2}$

= 2 ± √3

Roots are 2 + √3  , 2 - √3

Roots here are not rational but Irrational.

Hence Given Statement is False.

All quadratic equations whose discriminant is nonnegative have two rational roots is FALSE

Rational numbers are real numbers which can be written in the form p/q where p and q are integers and q≠0

All real numbers which are not rational  are irrationals.

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