Question

Write the quadratic polynomial whose sum and products of zeros are M+N and MN

Answer 1

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Given

Sum of zeroes = M + N

=> alpha + beta = M + N

and

Product of zeroes = MN

=> alpha × beta = MN

Required polynomial

$= > k(x {}^{2} - ( \alpha + \beta )x + \alpha \beta ) \\ \\ = > k(x {}^{2} - (m + n)x + mn) \\ \\ = > k( x{}^{2} - mx - nx + mn) \\ \\ \: \: \: where \: \: k \: \: is \: \: constant \\ \\ \\ = > x {}^{2} - mx + nx - mn.$


Hope it helps!

Answer 2

Final Answer:

The quadratic polynomial whose sum and products of zeros are M+N and MN, is $x^2+(M+N)x+MN=0$.

Given:

The sum and products of zeros of the quadratic polynomial are M+N and MN

To Find:

The quadratic polynomial whose sum and products of zeros are M+N and MN

Explanation:

The following points are vital to reach at the solution to this present problem.

• The zeros of the quadratic polynomial indicate the roots of the quadratic polynomial.

• The sum of the zeros of the quadratic polynomial $ax^2+bx+c=0$ is $=-\frac{b}{a}$.
• The products of the zeros of the quadratic polynomial $ax^2+bx+c=0$ is $=\frac{c}{a}$.

Step 1 of 2

As per the statement in the given problem, assume the zeros of the quadratic polynomial are $\alpha, \beta$.

So, in accordance with  the statement in the given problem, write the following equations.

$\alpha+\beta=-\frac{b}{a} =M+N\\\alpha\times \beta=\frac{c}{a} =M\times N$

Step 2 of 2

Thus it is evident that $(\alpha, \beta)=(M,N)$.

So, the quadratic polynomial whose sum and products of zeros are M+N and MN, is

$x^2+(M+N)x+MN=0$

Therefore, the required quadratic polynomial whose sum and products of zeros are M+N and MN, is $x^2+(M+N)x+MN=0$.

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