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Question
If the product of zeros of the polynomial f(x) ax3 − 6x2 + 11x − 6 is 4, then a =
Options
\[\frac{3}{2}\]
\[- \frac{3}{2}\]
\[\frac{2}{3}\]
\[- \frac{2}{3}\]
\[- \frac{2}{3}\]
Solution
Since `alpha` and`beta` are the zeros of quadratic polynomial f(x) ax3 − 6x2 + 11x − 6
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
So we have
`4 = ((-6)/a)`
`4 = 6/a`
`4a=6`
`a = 6/4`
`a= (3xxcancel(2))/(2xxcancel(2))`
`a = 3/2`
The value of a is `3/2`
Hence, the correct alternative is (a).
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