For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
Answers
Solution 1) :-
given that,
→ sum of zeros = (21/8)
→ product of zeros = (5/16)
so,
→ x² - (sum of zeros)x + product of zeroes = 0
→ x² - (21/8)x + (5/16) = 0
→ (16x² - 42x + 5) /16 = 0
→ 16x² - 42x + 5 = 0
now, factorising we get,
→ 16x² - 2x - 40x + 5 = 0
→ 2x(8x - 1) - 5(8x + 1) = 0
→ (8x - 1)(2x - 5) = 0
putting both equal to zero we get,
→ x = (1/8) and (5/2)
Solution 2) :-
given that,
→ sum of zeros = (-3/2√5)
→ product of zeros = (-1/2)
so,
→ x² - (sum of zeros)x + product of zeroes = 0
→ x² - (-3/2√5)x + (-1/2) = 0
→ x² + (3/2√5)x - (1/2) = 0
→ (2√5x² + 3x - √5) /2√5 = 0
→ 2√5x² + 3x - √5 = 0
now, factorising we get,
→ 2√5x² - 2x + 5x - √5 = 0
→ 2x(√5x - 1) + √5(√5x - 1) = 0
→ (√5x - 1)(2x + √5) = 0
→ x = (1/√5) and (-√5/2)
Learn more :-
JEE mains Question :-
https://brainly.in/question/22246812
. Find all the zeroes of the polynomial x4
– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.
https://brainly.in/question/39026698