Question

Find a quadratic polynomial whose zeroes are 1/2 , 4

Answer 1

The quadratic polynomial is x² - 4.5x + 2

Step-by-step explanation:

Zeros of quadratic polynomial are $\frac{1}{2}$, 4.

Let the quadratic polynomial = P(x)

$P(x) = (x - \frac{1}{2}) (x - 4)\\\\P(x) = x^{2} - 4x - \frac{x}{2} + 2\\\\P(x) = x^{2} - \frac{9x}{2} + 2\\\\P(x) = x^{2} - 4.5x + 2$

Hence, the quadratic polynomial is x² - 4.5x + 2

Answer 2

Given :  a quadratic polynomial whose zeroes are 1/2 , 4

To find : Quadratic  Polynomial

Solution:

a quadratic polynomial whose zeroes are 1/2 , 4

= (x - 1/2)(x - 4)

= x² - x/2 - 4x  + 2

= x² -9x/2 + 2

= 2x² - 9x  + 4

Another method

Zeroes  1/2  , 4

Sum of Zeroes = (1/2 + 4)  = 9/2

Product of Zeroes = (1/2)4 = 2

Polynomial

= x² - (Sum of roots)x + product of roots

= x² - (9/2)x  + 2

= 2x² -9x  + 4

2x² -9x  + 4 is a quadratic polynomial whose zeroes are 1/2 , 4

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