Question

find the zeroes of quadratic polynomialf(x) =mx(x-m-1) +m² verify the relationship between zeroes and its co efficient​

Answer 1

Answer:

x = m , 1

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros.

★ A quadratic polynomial can have atmost two zeros.

★ To find the zeros of the given polynomial , equate it to zero .

★ If A and B are the zeros of the quadratic polynomial p(x) = ax² + bx + c ; then ;

• Sum of zeros , (A+B) = -b/a

• Product of zeros , (A•B) = c/a

Solution:

Here ,

The given quadratic polynomial is ;

f(x) = mx(x - m - 1) + m²

The given quadratic polynomial can be rewritten as follow ↓

f(x) = mx² - m(m + 1)x + m²

Clearly ,

a = m

b = -m(m + 1)

c = m²

Now,

Let's find the zeros of the given quadratic polynomial by equating it to zero.

Thus,

=> f(x) = 0

=> mx² - m(m + 1)x + m² = 0

=> m•[x² - (m+1)x + m] = 0

=> x² - (m+1)x + m = 0

=> x² - mx - x + m = 0

=> x(x - m) - (x - m) = 0

=> (x - m)(x - 1) = 0

=> x = m , 1

Now,

Sum of zeros = m + 1

Also,

-b/a = - [-m(m + 1)] / m = m + 1

Clearly,

Sum of zeros = -b/a

Now,

Product of zeros = m•1 = m

Also,

c/a = m²/m = m

Clearly,

Product of zeros = c/a

Hence verified.