Question

quadratic polynomial the sum and product of zeros of 3 and -2​

Answer 1

Solution :-

We have to form a quadratic polynomial whoes :-

▪️Sum of roots = 3

▪️Product of roots = -2

Now as we know that

▪️Sum of roots = -b/a

▪️And product of roots = c/a

Then let the constant (a) be equal to k

Then

▪️Sum of roots = -b/k

or -b = k(Sum of roots)

or b = -k(Sum of roots)

or b = -k(S)

▪️Product of roots = c/k

or c = k(Product of roots)

or c = k(P)

Then we can represent a quadratic polynomial in the form of

kx² - Skx + Pk

or as k( x² - Sx + P)

So equation As S = 3 and P = -2

= k (x² -(3)x +(-2))

= k(x² - 3x - 2 )

or when k = 1

Polynomial = x² - 3x - 2

Answer 2

Correct question-

Find a quadratic polynomial whose product of zeroes is 3 and sum of zeroes is -2.

$\mathfrak{<u>The\: quadratic\: equation\: is</u><u>\</u><u>:</u><u>}</u><u>\</u><u>\</u><u> x^2+2x+3=0</u>$

We know

$\alpha+\beta=\frac{-b}{a}\\ \\ \therefore \alpha+\beta=(-2) --(1)\\ \\ and \ \alpha\beta=\frac{c}{a}\\ \\ \therefore \alpha\beta=3 --(2)$

Also, we know that a polynomial whose sum of zeroes and product of zeroes is given can be presented by

$x^2-(\alpha+\beta)x+(\alpha\beta)=0$

Well, we know that in this sum,

sum of zeroes is -2 and product of zeroes is 3.

So, putting the values from eq. (1) and (2) in the above equation we get

$</p><p>x^2-(-2)x+3=0\\ \\ x^2+2x+3=0$