The root
of
x2+kx+k=0
are real and equal . find k
Answers
EXPLANATION.
Quadratic equation.
⇒ x² + kx + k = 0.
As we know that,
D = Discriminant Or b² - 4ac.
Roots are real and equal : D = 0.
⇒ (k)² - 4(1)(k) = 0.
⇒ k² - 4k = 0.
⇒ k(k - 4) = 0.
⇒ k = 0 and k = 4.
MORE INFORMATION.
Nature of the roots of the quadratic expression.
(1) = Real and unequal, if b² - 4ac > 0.
(2) = Rational and different, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.
Given :-
The quadratic equation x²+kx+k=0 has real and equal roots
To find :-
Value of k
Solution :-
We know that some cases of nature of roots that were
If discriminant is equal to 0 then roots are real and equal
Discriminant of quadratic equation is b²-4ac
So,
b²-4ac = 0
Comparing with the general form of Quadratic equation ax²+bx+c =0
So,
a = 1
b = k
c= k
b²-4ac =0
(k)²-4(1)(k) = 0
k²- 4k =0
k(k-4) =0
k= 0
k-4 =0
k =4
So, the value of k is 4,0
Verification :-
Since we got value of k then the required quadratic equation is
- x²+4x+4
We shall find the roots of the quadratic equation by quadratic formula
-b±√ b²-4ac/2a
-4±√ (4)²-4(1)(4)/2(1)
-4±√ 16-16/2
-4±0/2
-4+0/2 , -4-0/2
-4/2 , -4/2
-2 , -2
Since the roots are -2, -2 i.e both are equal and real Since verified !
Know more :-
Discriminant of the Quadratic equation is b²-4ac .It helps to find the nature of the roots that means roots are real or conjugate or equal .
If a , b , c are real numbers
1) If D > 0 , then the roots are real and distinct.
2) If D = 0, then the roots are real and equal.
3) If D < 0 , then the roots are complex and conjugate to each other
If a , b , c are rational numbers
1) If D > 0 and 'D' is a perfect square then the roots are rational and distinct.
2) If D > 0 and 'D' not is a perfect square then the roots are irrational and conjugate to each other.
3) If D = 0 , then the roots are rational and equal.
4) If D < 0 , then the roots are not real and complex and conjugate to each other.