Find the zeros of 4√5x^2-17x-3√5 and verify the relation between the zeros and coefficient of the polynomial.
Answers
Answered by
113
heya..!!!
4√5x² - 17x + 3√5
=> 4√5x² - 12x - 5x + 3√5
=> 4x(√5x - 3) - √5(√5x - 3)
=> (4x - √5)(√5x - 3)
=> x = √5/4 = alpha and x = 3/√5 = beta
verification
alpha + beta = -b/a
=> √5/4 + -3/√5 = -(-17)/4√5
=> (5 + 12)/4√5 = 17/4√5
=> 17/4√5 = 17/4√5
r.h.s = l.h.s
and,
alpha×beta = c/a
=> √5/4 × 3/√5 = 3√5/4√5
=> 3/4 = 3/4
r.h.s = l.h.s
4√5x² - 17x + 3√5
=> 4√5x² - 12x - 5x + 3√5
=> 4x(√5x - 3) - √5(√5x - 3)
=> (4x - √5)(√5x - 3)
=> x = √5/4 = alpha and x = 3/√5 = beta
verification
alpha + beta = -b/a
=> √5/4 + -3/√5 = -(-17)/4√5
=> (5 + 12)/4√5 = 17/4√5
=> 17/4√5 = 17/4√5
r.h.s = l.h.s
and,
alpha×beta = c/a
=> √5/4 × 3/√5 = 3√5/4√5
=> 3/4 = 3/4
r.h.s = l.h.s
harmanbirkaur:
In the ques there is -3root 5 but u have written positive
Answered by
28
Answer:
Step-by-step explanation:
4√5x² - 17x + 3√5
=> 4√5x² - 12x - 5x + 3√5
=> 4x(√5x - 3) - √5(√5x - 3)
=> (4x - √5)(√5x - 3)
=> x = √5/4 = alpha and x = 3/√5 = beta
verification
alpha + beta = -b/a
=> √5/4 + -3/√5 = -(-17)/4√5
=> (5 + 12)/4√5 = 17/4√5
=> 17/4√5 = 17/4√5
r.h.s = l.h.s
and,
alpha×beta = c/a
=> √5/4 × 3/√5 = 3√5/4√5
=> 3/4 = 3/4
Rhs=lhs
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