Question

Q1.Ifthediscriminantofaquadraticpolynomial,D>0,thenthepolynomialhas (a)tworealandequalroots. (b)tworealandunequalroots (c)imaginaryroots. (d)noroot​

Answer 1

Given : A Quadratic polynomial Discriminant  D > 0

To Find :  Nature of the roots

a) two real and equal roots

b) two real and unequal roots

c) Imaginary roots

d) no roots

Solution:

Quadratic polynomial  is of the form ax²+bx+c  

where a  , b and c are real also  a≠0.

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

Hence correct option is

b) two real and unequal roots

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Answer 2

To Find :- If the discriminant of a quadratic polynomial, D > 0, then the polynomial has :-

(a) two real and equal roots.

(b) two real and unequal roots

(c) imaginary roots.

(d) no roots .

Solution :-

We know that, for a quadratic polynomial A•x^2 + B•x + C, its discriminant is given by :-

• D = B^2 - 4•A•C

now, we have three case :-

• If D = 0 , then the given quadratic polynomial has real and equal roots.

• If D > 0 , then the given quadratic polynomial has real and distinct roots .

• If D < 0 , then the given quadratic polynomial has unreal (imaginary) roots.

given that,

→ D > 0

since value of discriminant is greater than zero .The given quadratic polynomial has real and distinct (unequal) roots .

therefore, we can conclude that, the polynomial has Option (C) two real and unequal roots .

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