Question

Find a quadratic polynomial whose sum and product are -3/2root 5 and -1/2 respectively.

Answer 1

Step-by-step explanation:

sum of zeroes = -3/2√5

product of zeroes = -1/2

k[x²-(alpha+beta)x+(alpha)(beta)]

k[x²-(-3/2√5)x+(-1/2)

k[x²+3x/2√5-1/2]

k[2√5x²+3x-√5/2√5]

for k = 2√5

2√5[2√5x²+3x-√5/2√5]

therefore required quadratic polynomial is 2√5x²+3x-√5

Answer 2

Therefore the required quadratic polynomial whose sum and the product are -3/2√5 and -1/2 is '2√5x² + 3x - √5 = 0'.

Given:

Sum of the roots = -3/2√5

product of the roots = -1/2

To Find:

The quadratic polynomial whose sum and product are -3/2√5 and -1/2.

Solution:

The given question can be solved very easily as shown below.

Let α and β are the roots of the required polynomial.

Then, the quadratic polynomial becomes: 2√5x² + 3x - √5

⇒ p(x) = 2√5x² + 3x - √5

Sum of the roots = α +β = - b/a

⇒ -3/2√5 = -3/2√5

Product of the roots = αβ = c/a

⇒ -1/2 = -√5/2√5

⇒ -1/2 = -1/2

LHS = RHS

Therefore the required quadratic polynomial whose sum and the product are -3/2√5 and -1/2 is '2√5x² + 3x - √5 = 0'.

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