Find the quadratic polynomial each with given numbers as the sum and product of its zeros respectively. 1)-3, 2. 2)1, 1. 3)2, -3. 4)1/4,-1 .5)4, 1 Who answers this will be marked brainliest
Answers
Answer:
1) y = k(x² + 3x +2)
2) y = k[x² - x + 2]
3) y = k[x² - 2x - 3]
4) y = K[4x² - x + 8]
5) y = k[x² - 4x + 1]
Step-by-step explanation:
1) let α,β be the roots of the equation.
so according to the question,
α+β= -3, αβ = 2
as we know,
y = k[x²- (α+β)x + αβ] [ where k is a constant real number]
y = k[x² - (-3)x + 2]
y = k[x² + 3x +2] ⇒Equation required
{similarly,}
2) let α,β be the roots of the equation.
so according to the question,
α+β= 1, αβ = 1
as we know,
y = k[x²- (α+β)x + αβ] [ where k is a constant real number]
y = k[x² - 1x + 1]
y = k[x² - x + 2] ⇒Equation required
3) let α,β be the roots of the equation.
so according to the question,
α+β= 2, αβ = -3
as we know,
y = k[x²- (α+β)x + αβ] [ where k is a constant real number]
y = k[x² - 2x +(-3)]
y = k[x² - 2x - 3] ⇒Equation required
4) let α,β be the roots of the equation.
so according to the question,
α+β= 1/4, αβ = 5
as we know,
y = k[x²- (α+β)x + αβ] [ where k is a constant real number]
y = k[x² - (1/4)x + 5] {where K is another constant i.e. k=K/4]
y = K[4x² - x + 8] ⇒Equation required
[you can leave the equation with fractional coefficient as well]
5) let α,β be the roots of the equation.
so according to the question,
α+β= 4, αβ = 1
as we know,
y = k[x²- (α+β)x + αβ] [ where k is a constant real number]
y = k[x² - 4x + 1]
y = k[x² - 4x + 1] ⇒Equation required
hope it helps :)
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