Question

what is the Quadratic polynomial the sum of whose zeroes is-3÷2 and the product of the zeroes is -1
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Answer 1

$\large \dag$ Question :-

what is the Quadratic polynomial the sum of whose zeroes is $\sf\dfrac{ - 3}{ \: \: 2}$

and the product of the zeroes is -1

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Polynomial   \:  is \:  2x^2+3x-2}} }$

$\large \dag$ Step by step Explanation :-

❒ We Know that general form of any quadratic polynomial is :

$\red \bigstar \small \: \blue{\bigg \{ \underline{ \overline{\boxed{\rm {x}^{2} - (Sum \: of \: zeros)x + Product \: of \: zeros}}} \bigg\}}$

☆ Here in this question we have ;

• Sum of Zeros = $\sf\dfrac{ - 3}{ \: \: 2}$

• Product of Zeros = $\sf-1$

⏩ Substituting values in general form of quadratic polynomial ;

$\small:\longmapsto \rm Req{}^{d}. \: Poly nomial = {x}^{2} - \bigg( \frac{ - 3}{ \: \: 2} \bigg)x + ( - 1)$

$:\longmapsto \rm Req{}^{d}. \: Poly nomial = {x}^{2} + \frac{3}{2} x - 1$

$: \green{\longmapsto\underline{\underline{{ \purple{ \rm Req{}^{d}. \: Poly nomial =2x^2+3x-2 }}}}}$

$\large \dag$ Additional Information :-

❒ Quadratic Polynomial with one Variable :

✪ The general form of the equation is ax² + bx + c = 0.

• If a = 0, then the equation becomes to a linear equation.

• If b = 0, then the roots of the equation becomes equal but opposite in sign.

• If c = 0, then one of the roots is zero.

❒ Nature Of Roots :

✪ b² - 4ac is the discriminate of the equation Then ,

• If b² - 4ac = 0, then the roots are real & equal.

• If b² - 4ac > 0, then the roots are real & unequal.

• If b² - 4ac < 0, then the roots are imaginary & no real roots.

Answer 2

QUESTION-:

what is the Quadratic polynomial the sum of whose zeroes is-3/2 and the product of the zeroes is -1

EXPLANATION-:

Let the roots of the given quadratic equation be -:

α & β

According to the given condition-:

α+β=-3/2 ,αβ=-1

We know that,Quadratic polynomial is -:

$\bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ \bf\; \blue{ x^2-(\alpha +\beta)x-(\alpha \beta)}}}}$

Polynomial so formed-:

$\rightarrow \bf\; x^2-(-\frac{3}{2}x)+(-1)\\\\\rightarrow \bf\; x^2+\frac{3}{2}x-1$

So the quadratic equation is-:

$\dashrightarrow \underline{\boxed{\bf\;x^2+\frac{3}{2}x-1 }}$

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