Question

23. A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively is *

1 point


. A quadratic polynomial, whose zeros are 5 and -8 is
​

Answer 1

$\rm\huge\blue{\underbrace{ Questions : }}$

(1) A quadratic polynomial with 3 and 2 as the sum and product of its zeros respectively is..?

(2) A quadratic polynomial, whose zeros are 5 and -8 is..?

$\rm\huge\blue{\underbrace{ Solutions : }}$

(1)

★ Given that,

• Sum of the zeroes : α + ß = 3
• Product of the zeroes : αß = 2

★ To find,

• The quadratic polynomial.

★ Let,

The general form of the quadratic polynomial is :

• $\tt\green{ : \implies x^{2} - (\alpha + \beta)x + (\alpha\beta) = 0}$
• Substitute the zeroes.

$\sf\:\implies x^{2} - (3)x + (2) = 0$

$\sf\:\implies x^{2} - 3x + 2 = 0$

$\underline{\boxed{\bf{\purple{ \therefore The\:Quadratic\: Polynomial\:is \: x^{2} - 3x + 2 = 0}}}}\:\orange{\bigstar}$

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(2)

★ Given that,

• Zeroes of quadratic polynomial is 5 , - 8

★ To find,

• The quadratic polynomial.

★ Let,

• Alpha (α) = 5
• Beta (ß) = - 8

$\tt\green{ :\implies Sum\:of\:the\:zeroes= \alpha + \beta = 5 + (-8) = 5 - 8 = - 3 }$

$\tt\green{ :\implies Product\:of\:the\:zeroes= \alpha\beta = 5 (-8) = - 40 }$

Hence,

1. α + ß = - 3
2. αß = - 40

The general form of quadratic polynomial is

• $\tt\green{ : \implies x^{2} - (\alpha + \beta)x + (\alpha\beta) = 0}$
• Substitute the zeroes.

$\sf\:\implies x^{2} - (-3)x +(-40) = 0$

$\sf\:\implies x^{2} + 3x - 40 = 0$

$\underline{\boxed{\bf{\purple{\therefore The\:Quadratic\:Polynomial\:is\:x^{2} + 3x - 40 = 0}}}}\:\orange{\bigstar}$

Answer 2

Answer:

x^2-3x-40=0

Step-by-step explanation:

x^2 - (alpha + beta )

$\alpha + \beta x + \alpha \beta$