If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 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
Solution:
Given, the quadratic polynomial is ax² + bx + c.
Given, c is not equal to zero.
The zeros of the quadratic polynomial are equal.
We have to find whether the zeros of the polynomial have the same or opposite signs.
Since the zeros of the polynomial are equal, the value of the discriminant will be equal to zero.
Discriminant = b² - 4ac
b² - 4ac = 0
b² = 4ac
Since b² cannot be negative, 4ac also cannot be negative.
Therefore, a and c both must be of the same sign.
✦ Try This: If the zeroes of the quadratic polynomial rx² + sx + t, t≠0 are equal, then
Given, the quadratic polynomial is rx² + sx + t
Given, t is not equal to zero.
The zeros of the quadratic polynomial are equal.
We have to find whether the zeros of the polynomial have the same or opposite signs.
Since the zeros of the polynomial are equal, the value of the discriminant will be equal to zero.
Discriminant = b² - 4ac
b² - 4ac = 0
b² = 4ac
Here, a = r, b = s and c = t
So, s² = 4rt
Since s² cannot be negative, 4rt also cannot be negative.
Therefore, r and t both must be of the same sign
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.1 Problem 9
If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 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
Summary:
If the zeroes of the quadratic polynomial ax² + bx + c, c≠0 are equal, then a and c must have the same sign
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