Question

if a and b are the zeroes of the polynomial x2 + 4x + 3 ,form the polynomial whose zeroes are 1 + b/a and 1 + a/b​

Answer 1

Answer:

Since α and β are the zeros of the quadratic polynomial x2+4x+3

Then, α+β=−4,αβ=3

Now, the of sum of the zeros of new polynomial is

=1+αβ+1+βα=αβαβ+β2+αβ+α2

=αβα2+β2+2αβ=αβ(α+β)2=3(−4)2=316

Also, Product of the zeros of new polynomial is

=2+αβα2+β2=αβ2αβ+α2+β2

=αβ(α+β)2=3(−4)2=316

Therefore, the required polynomial is

k×

Answer 2

Hello there !

Question:-

• if a and b are the zeroes of the polynomial x2 + 4x + 3 ,form the polynomial whose zeroes are 1 + b/a and 1 + a/b

Answer:-

we have the equation:-

x²+4x+3

By splitting the middle term,

x²+4x+3

x²+(3+1)x+3

x²+3x+x+3

x(x+3)+1(x+3)

(x+3)(x+1)

therefore :

a = -3 and b = -1

according to the zeroes we have:-

$\frac{1 + b}{a} \: \: and \: \frac{1 + a}{b}$

let us put the values we got,

$\frac{1 + b}{a} = \frac{1 + ( - 1)}{ - 3} = \frac{1 - 1}{ - 3} = 0 \\ hence \: \: \alpha = 0$

and....

$\frac{1 + a}{b} = \frac{1 + ( - 3)}{ - 1} = \frac{1 - 3}{ - 1} = \frac{ - 2}{ - 1} = 2 \\ hence \: \: \beta = 2$

now,

• sum of the zeroes = 0+2 = 2
• product of zeroes = 0(2) = 0

So, to find the polynomial;

p(X) = x²- sum of zeroes + product of zeroes

= x²-2x+0

= x²-2x

Hence, the required polynomial is x²-2x.

______________________________

Hope it helps ⭐⭐⭐