Question

If the product of the zeroes of the polynomia
ax2 - 6x² +11x-6 is 6, then the value of a is​

Answer 1

Given:

• the product of the zeroes of the polynomia
• ax2 - 6x² +11x-6 is 6.
• therefore, Let the zeroes α and β
• xy = 6

To Find:

• value of a

Solution:

$\sf \: we \: have \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\sf \alpha \beta = 6}$

$\sf \: also \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf \alpha \beta = \frac{c}{a} }$

Therefore by comparing eq. with general form

we get,

$\: \: \: \: \: \: \: \: \: \: \: \: \sf \: a = (a - 6) \\ \sf \: b = 11 \\ \: \: \: \: \: \sf \: c = ( - 6)$

Now,

$\sf \: \frac{c}{a} = 6 \\ \\ \rightarrow \sf \: \frac{( - 6)}{(a - 6)} = 6 \\ \rightarrow \sf - 6 = 6a - 36 \\ \rightarrow \sf 30 = 6a \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \red{a = 5}}$

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