Question

Form a quadratic polynomial whose one of the reroes is +15 and sum of the zeroes is 42.

Answer 1

Let one zeros be x

• Sum of the Zeros is 42

x + 15 = 42

x = 42 - 15

x = 27

• Product of Zeros :-

27 × 15

= 405

♯ To form a quadratic equation when sum and product of Zeros is known :-

x² - ( Sum of Zeros )x + (product of Zeros)

Putting values in it ¡

x² - 42x + 405 = 0 is the required quadratic equation !!

Answer 2

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♦ QUADRATIC POLY. ♦

→ Recall Viete's Relation [ Coefficient-root relation ] :
    • Sum of roots = [ - Coeff.( x ) ] / [ Coeff( x² ) ]
    • Product of roots = [ Constant Term ] / [ Coeff( x² ) ]

→ Given the sum of roots as 'S'
→     The sum of products as 'P'

◘ The Quadratic Polynomial is : F(x) = [ x² - Sx + P ]

→ Here, Quadratic Poly. is : P(x) = [ x² - 42x + P ] 

• Sum of zeroes = 42 ; One zero = 15 => Other Zero = 27

♦ Desired Poly. is :   P( x ) = [ x² - 42x + ( 15 )( 27 ) ] 
                                          = [ x² - 42x + 405 ]
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^_^ Hope it helps