Question

1.If α and β are zeroes of the polynomial x²-2x-15 then form a quadratic polynomial whose zeroes 2α and 2β. 2.If the sum of the zeroes of the polynomial f(t)=kt²+2t+3k is equal to the product then the value of k is________? 3.Find the value of a for which (x-a) is a factor of f(x) =-x³+ax²+3x+9. 4.If x-a/b+a + x-b/c+a + x-c/a+b = 3 then the value of x is______?




it's Isha
gm to all​

Answer 1

Answer:

see the attachment.

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Answer 2

Answer:

Given α,β are the zeroes of the quadratic polynomial x2−2x−15.

General form of a quadratic polynomial is

x2−(Sum of zeroes)x+(Product of zeroes).

For the given polynomial,

Sum of zeroes = α+β=2⋯(1)

Product of zeroes = αβ=−15⋯(2)

We need to find a new quadratic polynomial whose zeroes are 2α,2β.

Let's find the sum of zeroes and product of zeroes in order to form the polynomial.

Sum of zeroes = 2α+2β=2(α+β)=2×2=4

[From (1)]

Product of zeroes = 2α×2β=4αβ=4×(−15)=−60

[From (2)]

Therefore the required quadratic polynomial is: x2−4x−60.

Step-by-step explanation:g.m