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Question
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
3x2 – x – 4
Solution
3x2 – x – 4
= 3x2 – 4x + 3x – 4
= x(3x - 4) + 1(3x - 4)
= (3x - 4)(x + 1)
For p(x) = 0 we have,
Either (x + 1) = 0
x = -1
or 3x - 4 = 0
`x = 4/3`
∴ The zeroes of 3x2 - x - 4 are -1 and `4/3`
Now,
Sum of the zeroes = `-("Coefficient of " x)/("Coefficient of " x^2)`
= `(-1) + 4/3`
= `(-(-1))/3`
= `1/3 = 1/3`
and product of zeroes `"Constant term"/("Coefficient of " x^2)`
`(-1)xx 4/3 = (-4)/3`
= `(-4)/3 = (-4)/3`
Thus, the relationship between the zeroes and coefficients in the polynomial 3x2 - x - 4 is verified.
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