Question

If zeroes of polynomial 2x^2-3x+lambda and ax^2-6x+u are same then find the value of :lambda×a/u

Answer 1

Answer:

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Answer 2

Given,

$\[\begin{array}{l}2{x^2} - 3x + \lambda \\a{x^2} - 6x + \mu \end{array}\]$

Solution,

Formula used, sum of roots$\[ = \frac{b}{a}\]$

Formula used, Product of the roots$\[ = \frac{c}{a}\]$

Know that here the equations have same zeros.

So, the sum of the roots are

$\[\begin{array}{l} \Rightarrow - \frac{3}{2} = \frac{1}{2} + \alpha \\ \Rightarrow \alpha = - \frac{3}{2} - \frac{1}{2}\\ \Rightarrow \alpha = - \frac{4}{2}\\ \Rightarrow \alpha = - 2\end{array}\]$

So, the product of the roots are

$\[\begin{array}{l} \Rightarrow \frac{\lambda }{2} = - 2 \times \frac{1}{2}\\ \Rightarrow \lambda = 2 \times - 2 \times \frac{1}{2}\\ \Rightarrow \lambda = - 2\end{array}\]$

Therefore,

$\[\begin{array}{l} \Rightarrow \alpha \times \lambda \\ \Rightarrow - 2 \times - 2\\ \Rightarrow 4\end{array}\]$

Hence, the required value is $\[4.\]$