Find the value of K for
which the roots of quadratic
equation are real and equal
4x²-3kx+1=0
Answers
Question :
Find the value of k for which the roots of quadratic equation are real and equal 4x²-3kx+1=0
Theory :
For a Quadratic equation of the form
ax²+bx+c= 0 , the expression b²-4ac is called the discriminant.
Nature of roots
The roots of a quadratic equation can be of three types.
- If D>0, the equation has two distinct real roots.
- If D=0, the equation has two equal real roots.
- If D<0, the equation has no real roots.
Solution :
We have , 4x²-3kx+1=0
On comparing with the standard form of Quadratic equation ax²+bx+c= 0.
Here ,
a= 4
b = -3k
and c = 1
For equal and real roots ;
Discrimant = 0
Therefore , The value of k = -4/3 or 4/3
Answer:
Given :-
- The roots of qradratic equation are real and equal is 4x² - 3kx + 1 = 0
To Find :-
- What is the value of k.
Solution :-
Given equation :
4x² - 3kx + 1 = 0
where, a = 4, b = - 3k, c = 1
Since, the roots are real and equal.
The discriminant = 0
b² - 4ac = 0
=> (- 3k)² - 4.4.1 = 0
=> 9k² - 16 = 0
=> (3k)² - (4)² = 0
=> (3k + 4)(3k - 4) = 0
=> 3k + 4 = 0 ; 3k - 4 = 0
=> 3k = - 4 ; 3k = 4
=> k = ; k =
k = ,