Question

A quadratic polynomial whose one zero is 5 and product of zeros is 0 is

Answer 1

Let the zeros of the polynomial be x and y

ATQ,

x= 5
xy = 0

⇒y = 0


So the required polynomial with zeros x and y is

x²- (5+0)x + (5* 0) = 0
x² - 5x + 0 = 0

x² - 5x = 0

Answer 2

x² - 5x  is a quadratic polynomial whose one zero is 5 and product of zeros is 0

Given:

• A quadratic polynomial
• One zero is 5
• Product of Zeroes is 0

To Find:

• A Quadratic polynomial

Solution:

Quadratic polynomial is of the form ax²+bx+c   where a  , b and c are real and   a≠0.

A polynomial with zeroes α and β can be represented as:

P(x) = k(x - α)(x -β )  where k is non zero real number

Step 1:

Assume one zero  α = 5

Other zero β

Step 2:

Equate product of zeroes with 0 , substitute α = 5 and solve for  β

αβ= 0

5β= 0

β=0

Step 3:

Find generalized polynomial

P(x) = k(x - α)(x -β )

p(x) = k(x - 5)(x - 0)

p(x) = k ( x² - 5x)

Step 4:

Find a polynomial by substituting k = 1

p(x) = 1  ( x² - 5x)

p(x) = x² - 5x

x² - 5x  is a quadratic polynomial whose one zero is 5 and product of zeros is 0

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