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