Find a quadratic polynomial, the sum and product of whose zeros are7/2 -5/4
respectively.
Answers
Answer:
Given:- The sum of the zeroes are -7. The product of the zeroes are 2. To Find:- The quadratic polynomial. Solution:- We Know , ...
= = 2.
The sum of zeroes = α + β =
= = -7. so, the required polynomial becomes. = k[ x² + ( α + β ) - (αβ) ] = k [ x² + ( -7 ) - ( 2) ] = k [ x² - 7 - 2 ]
EXPLANATION.
Quadratic polynomial,
Sum of the zeroes of quadratic equation = 7/2
Products of the zeroes of quadratic equation = -5/4.
As we know that,
General equation of quadratic polynomial,
⇒ ax² + bx + c = 0.
Sum of zeroes of quadratic equation.
⇒ α + β = -b/a.
⇒ α + β = 7/2.
Products of zeroes of quadratic equation.
⇒ αβ = c/a.
⇒ αβ = -5/4.
Quadratic polynomial,
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (7/2)x + (-5/4) = 0.
⇒ x² - 7x/2 - 5/4 = 0.
⇒ 4x² - 14x - 5 = 0.
MORE INFORMATION.
Nature of the factors of the quadratic expression.
(1) = Real and different, 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.