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Find the zeros of the quadratic polynomial 6x^2 - 13x + 6 and verify the relation between the zero and its coefficients. - Mathematics

Sum

Find the zeros of the quadratic polynomial 6x2 - 13x + 6 and verify the relation between the zero and its coefficients.

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Solution

We have, 6x2 -13x + 6 = 6 x 2 - 4x - 9x + 6

= 2x(3x - 2) - 3(3x -2)

= (3x - 2) (2x - 3)

So, the value of 6x2 - 13x + 6 is 0 when

(3x - 2) = 0 or (2x - 3) = 0 i.e.,

When x = `2/3` or `3/2`

Sum of the zeros

=`2/3+3/2=13/6=-((-13))/6= -["coefficient of x"/("coefficient of "x^2)]`

Product of the zeros 

=`2/3xx3/2=6/6 =["coefficient of x"/("coefficient of "x^2)]`

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