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Question

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 factorization.
(i) -83, 43    (ii) 218, 516   (iii)   -23, -9     (iv)  -325,  -12Question


Solution

We know that a quadratic polynomial whose sum and product of zeroes are given is
fx=kx2-Sum of zeroesx+Product of zeroes

(i) We have, sum of zeroes = -83 and product of zeroes = 43
So, the required quadratic polynomial will be fx=kx2+83x+43
fx=kx2+83x+43=k33x2+8x+4=k33x2+6x+2x+4=k33xx+2+2x+2=k33x+2x+2
Now, the zeroes are given by f(x) = 0.
Thus, x=-23 and x=-2
(ii) We have, sum of zeroes = 218 and product of zeroes = 516
So, the required quadratic polynomial will be fx=kx2-218x+516
fx=kx2-218x+516=k1616x2-42x+5=k1616x2-40x-2x+5=k1616x2-2x-40x+5=k32x8x-1-58x-1=k38x-12x-5
Now, the zeroes are given by f(x) = 0.
Thus, x=18 and x=52
(iii) We have, sum of zeroes = -23 and product of zeroes = −9.
So, the required quadratic polynomial will be fx=kx2+23x-9.
fx=kx2+23x-9=kx2+33x-3x-9=kx+33x-3
Now, the zeroes are given by f(x) = 0.
Thus, x=-33 and x=3.

(iv) We have, sum of zeroes = -325 and product of zeroes = -12
So, the required quadratic polynomial will be fx=kx2+325x-12.
fx=k2525x2+3x-5=k2525x2+5x-2x-5=k255x2x+5-12x+5x=k252x+55x-1

Now, the zeroes are given by f(x) = 0.
Thus, x=-52 and x=15.

Mathematics
RD Sharma (2016)
Standard X

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