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  • If the zeroes of the quadratic polynomial ax^2 + bx + c, c 0 are equal, then (A) c and a have opposite signs

If the zeroes of the quadratic polynomial ax^2 + bx + c, c \neq 0 are equal, then

(A) c and a have opposite signs

(B) c and b have opposite signs

(C) c and a have the same sign

(D) c and b have the same sign

Answers (1)

Answer. [C]

Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s) and a quadratic polynomial is polynomial of degree 2.

Here the given polynomial is ax^2 + bx + c, c \neq 0

a = a, b = b, c = c

We know that if both the zeroes are equal there

b^2 - 4ac = 0  

b^2 =4ac     ….(1)

(A) c and a have opposite sign

If c and a have opposite sign then R.H.S. of equation (1) is negative but L.H.S. is always positive. So (A) is not a correct one.

(B) c and b have opposite sign

If c is negative and b is positive L.H.S. is positive but R.H.S. of eqn. (1) is negative. Hence (B) is not correct one.

(C) c and a have same sign

If c and a have same sign R.H.S. of eqn. (1) is positive and L.H.S. is always positive hence it is a correct one.

(D) c and b have same sign

If c and b both have negative sign then R.H.S. of eqn. (1) is negative and L.H.S. is positive. So this is not correct.

Only one option i.e. (c) is correct one.

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infoexpert21

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