Question

Topic - Zeros of Algebric Expression.

Question - Zeros of a quadratic polynomial are 4 and -3.

♡Find the quadratic polynomial ♡​

Answer 1

Given :-

Zeros of a quadratic polynomial are 4 and -3

To Find :-

Qudratic polynomial

Solution :-

Finding sum of zeroes

4 + (-3) = 4 - 3 = 1

Finding product of zeroes

4 × -3 = -12

Now

Standard form of quadratic polynomial = x² - (α + β)x + αβ

⇒ x² - (1)x + (-12)

⇒ x² - 1x - 12

⇒ x² - x - 12

Hence

Required polynomial is x² - x - 12

Verification :-

x² - x - 12 = 0

x² - (4x - 3x) - 12 = 0

x² - 4x + 3x - 12 = 0

x(x - 4) + 3(x - 4) = 0

(x - 4)(x + 3) = 0

Finding zeroes

x - 4 = 0

x = 0 + 4

x = 4

x - 3 = 0

x = 0 - 3

x = -3

Hence verified

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Answer 2

Answer :

• $\longmapsto \bf {x}^{2} - x - 12$

___________

As per the information given in the question, We have :

• Zeros of a quadratic polynomial are 4 and -3.

We are asked to calculate the quadratic polynomial.

Here, First let us consider the zeroes of be 4 & -3. And then, As we know that, Quadratic Polynomial is in the form of ax² + bx + c.

In order to form the Polynomial in this form, We will find sum of zeroes and product of zeroes. Then we will put those values in this formula → x² - (Sum of Zeroes)x + (Product of zeroes).

Calculating sum of zeroes :

${ \longmapsto \rm 4 + ( - 3)}$

Performing addition with the numbers.

${ \longmapsto \bf 1}$

∴ Sum of zeroes is 1.

$\rule{200}2$

Calculating product of zeroes :

${ \longmapsto \rm 4 \times ( - 3)}$

Performing multiplication with the numbers.

${ \longmapsto \bf - 12}$

∴ Product of zeroes is -12.

$\rule{200}2$

Finding the quadratic polynomial :

${ \longmapsto \rm {x}^{2} - (Sum \: of \: Zeroes)x + (Product \: of \: zeroes)}$

Putting the values,

$\longmapsto \rm {x}^{2} - (1)x + ( - 12)$

On Simplifying,

$\longmapsto \bf {x}^{2} - x - 12$

∴ The required quadratic polynomial is x² - x - 12.

Points to remember :

• The standard form of a quadratic polynomial is $\bf {ax}^{2} + bx + c = 0$. Where a ≠ 0.

• You can find the quadratic polynomial by squaring too. The word quadratic comes from the word "Quadratum" Which means square.