Question

Find the quadratic polynomial whose zero are 2by3 and 1by2​

Answer 1

Here’s ur answer.

(X-2/3)(x+1/4)=0

(3x-2)(4x-1)=0

12x^2-5x-2=0

verification

Sum of zeroes= b/a

2/3x(-1/4)=(5/12)

2/3x(-1/4)=(-2/12)

Hence proved!

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Answer 2

Let the zeros of the required quadratic polynomial br a and b.

Since, a = 2/3 & b = 1/2.

sum of zeros = a + b = 2/3 + 1/2 = 7/6

product of zeros = ab = 2/3 x 1/2 = 2/10 = 1/5.

Required equation is,

$x ^{2} - (a + b)x + ab = 0$

x^2 - 7/6 x + 1/5 = 0

30x^2 - 35x + 6 = 0