Question

The quadratic polynomial whose sum and difference of zeroes are 4 and 6
respectively, is
(a)x2+4x+6
(b) x2-4x+6
(c) x2-4x-5 '
(d)x2-4x+5

Answer 1

Answer:

alpha+bita=4

alpha×bita = 6

formula= x²+(alpha+bita)x+(alpha×bita)

so, x²+(4)x+(6)

which gives -> x²+4x+6

the answer is option c).

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The quadratic polynomial whose sum and difference of zeroes are 4 and 6 respectively is

(a) x² + 4x + 6

(b) x² - 4x + 6

(c) x² - 4x - 5

(d) x² - 4x + 5

EVALUATION

Let the zeroes of the quadratic polynomial are α and β

Now by the given

α + β = 4 - - - - - (1)

α - β = 6 - - - - - (2)

Adding Equation 1 and Equation 2 we get

2α = 10

⇒ α = 5

From Equation 1 we get

β = 4 - 5 = - 1

Thus we have

Sum of the zeroes = α + β = 4

Product of the zeroes = αβ = - 5

Hence the required Quadratic polynomial is

= x² - ( α + β )x + αβ

= x² - 4x - 5

FINAL ANSWER

Hence the correct option is (c) x² - 4x - 5

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