Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively.
$3,1$

• A. $x^2-4x+3$
• B. $x^2+3x+1$
• C. $x^2-3x+1$
• D. None of these

Answer 1

The correct option is C $x^2-3x+1$

Let the polynomial be,

$\Rightarrow$ $p\left(x\right)=a{x}^2+bx+c$ ------ ( 1 )

$\Rightarrow$ Sum of zeros $=3$

$\therefore$ $-\frac{b}{a}=3$

Let $a=1$,

$\therefore$ $-\frac{b}{1}=3$

$\therefore$ $b=-3$

$\Rightarrow$ Product of zeros $=1$

$\therefore$ $\frac{c}{a}=1$

Let $a=1$

$\therefore$ $c=1$

Now, substituting $a=1,b=-3$ and $c=1$ in equation ( 1 ), we get

$\Rightarrow$ $x^2-3x+1$

$\therefore$ The required quadratic polynomial is $x^2-3x+1$