1.

Form a quadratic polynomial one of whose zero is√5and the product of the zeros is -2√5​

Answer»

ANSWER:

  • Required polynomial = x²-(√5-2)x-2√5

GIVEN:

  • FIRST zero (α) = √5.
  • Product of ZEROS (αβ) = -2√5.

TO FIND:

  • A quadratic polynomial.

SOLUTION:

=> First zero (α) = √5.

Finding second zero (β)

=> Product of zeros (αβ) = -2√5

=> (√5)*(β) = -2√5

=> β = -2√5/√5

=> β = -2

Sum of zeros (α+β):

= √5+(-2)

= √5-2

Standard FORM of Quadratic polynomial when Zeros are given:

= x²-(α+β)x+αβ. ....(i)

PUTTING the values in eq (i)

= x²-(√5-2)x+(-2√5)

= x²-(√5-2)x-2√5

NOTE:

Some important formulas:

=> Sum of zeros (α+β) = -(Coefficient of x)/Coefficient of x²

=> Product of zeros (αβ) = Constant term/ Coefficient of x²


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