Question

21. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and -2​

Answer 1

$\Huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Solution :

Let the zeroes be α (alpha) and β (beta)

If we are given,

• Sum of zeros = 3
• Product of zeroes = -2

So,

α + β = 3 -----(1)

And

α*β = -2 -------(2)

$\rule{100}{2}$

We have formula for finding quadratic polynomial :

$\Large{\boxed{\boxed{\red{\sf{a[x^2 \: - \: (\alpha \: + \: \beta)x \: + \: (\alpha \: \times \: \beta)]}}}}}$

(Putting Values)

⇒ Polynomial = x² - 3x + (-2)

⇒ Polynomial = x² - 3x - 2

Polynomial is,

$\Large \implies {\boxed{\red{\sf{x^2 \: - \: 3x \: - \: 2}}}}$

$\rule{200}{2}$

Additional information

• A polynomial with one degree is called Linear Polynomial.

Example = 2x - 3 , x + 3

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• A polynomial of two degree is called Quadratic Polynomial.

Example = 5x² + 3x -2 , 2x² + 6

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• A polynomial of three degree is called Cubic Polynomial.

Example = x³ , x³ + x² - 3x + 5

Answer 2

Answer: x² - 3x - 2

Step-by-step explanation:

We have given,

Sum of roots of quadratic polynomial is 3 and Product roots of quadratic polynomial is -2

We know that if  the roots of a quadratic polynomial are α and β. Then quadratic polynomial will be of the form as,

p(x) = x² -(α + β) + αβ  

In this question,

α + β = 3

αβ  = -2

Putting these values of (α+β)  and αβ in p(x)

We get,

p(x) = x² - (3)x + (-2)

p(x) = x² - 3x - 2

p(x) = x² - 3x - 2

This is the required quadratic polynomial