Question

A quadratic equation ax²+bx+c=0has i) two equal roots, if b²-4ac _____ ii) two distinct real roots, if b²-4ac___0​

Answer 1

Answer :

A quadratic equation ax²+bx+c=0 has

i) two equal roots, if b²-4ac = 0

ii) two distinct real roots, if b²-4ac > 0

Step-by-step explanation:

Quadratic Polynomials :

• A polynomial of degree 2
• General equation,

ax² + bx + c = 0

• Relation between zeros and coefficients :

Sum of zeroes = -b/a

Product of zeroes

• Nature of roots is determined by the value of discriminant.

D = b² - 4ac

If D = 0 ; the roots are real and equal.

If D > 0 ; the roots are real and distinct.

If D < 0 ; the roots are not real.

Therefore,

A quadratic equation ax²+bx+c=0 has

i) two equal roots, if b²-4ac = 0

ii) two distinct real roots, if b²-4ac > 0

Answer 2

$\huge\bf\underline\red{Explanation:-}$

In quadratic equation The equation has two roots We can know the nature of roots based on Discriminant

In Quadratic equation Discriminant is b²-4ac It is denoted by D or delta

Nature of roots

If D>0 Roots are Real and distinct

D=0 Roots are Equal and Real

D<0 Roots are complex (not real) and conjugate to each other

________________________________________________________

So, Given that

Roots are equal So,b²-4ac=0

Roots are real and distinct So, b²-4ac>0