A quadratic polynomial, whose zeroes are -3 and 4, is (a) x²- x + 12 (b) x² - x - 12 (c) 2x² - 2x – 12 (d) 2x² + 2x – 24
Answers
EXPLANATION.
Quadratic polynomial.
Whose zeroes are = - 3 and 4.
As we know that,
Let one zeroes be = - 3 = α.
Other zeroes be = 4 = β.
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ (-3) + (4) = 1.
⇒ α + β = 1. - - - - - (1).
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ (-3) x (4) = - 12.
⇒ αβ = - 12.
As we know that,
Formula of quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (1)x + (-12).
⇒ x² - x - 12.
Option [B] is correct answer.
MORE INFORMATION.
Nature of the roots of the quadratic expression.
(1) = Real and unequal, if b² - 4ac > 0.
(2) = Rational and different, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.
Given :-
A quadratic polynomial, whose zeroes are -3 and 4
To Find :-
Quadratic polynomial
Solution :-
Sum of zeroes = α + β
Sum = -3 + 4
Sum = 1
Product of zeroes = αβ
Product = -3 × 4
Product = -12
Now,
Standard form of quadratic polynomial = x² - (α + β)x + αβ
Quadratic polynomial = x² - (1)x + (-12)
Quadratic polynomial = x² - x - 12
Therefore
Option B is correct
V e r i f i c a t i o n :
x² - x - 12
x² - (4x - 3x) - 12
x² - 4x + 3x - 12
x(x - 4) + 3(x - 4)
(x - 4)(x + 3)
Either
x - 4 = 0
x = 4
or,
x + 3 = 0
x = -3