Question

Find a quadratic polynomial whose zeroes are 3 and 4​

Answer 1

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Quadratic equation with α and β as roots can be written as

x² − ( α + b ) + αb = 0

Here, 

α = −3 

b = 4

∴α + b = −3 + 4 =,1

and 

α − b = −3 × 4

= −12

∴ The quadratic equation is

x² − ( α + b )x + ab = 0

⇒ x²−1x−12=0

⇒ x²/2 - x/2 - 12/2 = 0

⇒ x²/2 - x/2 - 6 = 0

Hence,

The quadratic polynomial is 2x²−2x−6

Answer 2

EXPLANATION.

Quadratic polynomial whose zeroes are = 3 and 4.

let α and β are the zeroes of the polynomial.

sum of zeroes of quadratic polynomial,

⇒ α + β = -b/a.

⇒ -3 + 4 = 1.   ........(1)

product of zeroes of quadratic polynomial.

⇒ αβ = c/a.

⇒ (-3)(4) = -12.  ........(2).

quadratic polynomial whose zeroes are α and β,

⇒ x² - (α+β) + αβ.

⇒ x² - ( 1)x + (-12).

⇒ x² - x - 12 = 0.

MORE INFORMATION.

(1) = D > 0 Or b² - 4ac > 0 [ roots are real and unequal ].

(2) = D = 0 Or b² - 4ac = 0 [ roots are real and equal].

(3) = D < 0 Or b² - 4ac < 0 [ roots are imaginary ].