1) trying to fit it into the pattern of the square of a binomial (“completing the square”) to look like (x+y)2=x2+2xy+y2(x+y)2=x2+2xy+y2
2) remembering that a quadratic equation has 2 equal real roots when the discriminant is zero, so Delta=b2–4ac=0Delta=b2–4ac=0
For 1) rewrite the equation, dividing both sides by 3:
…which would correspond to the square:
…and comparing coefficients of x from last line, this leads to k=±4k=±4
For solution 2) you will have 3k2−48=0⟹k=±
a=3 ,b= - k root3 ,c=4
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For the quadratic equation to have real roots.
k = 4.5/2
alpha * beta =4/3
Hope It Helps
The value of k is
The given quadratic equation is
We have given that, the given quadratic equation has real and equal roots.
It means the value of discriminant must be 0.
Therefore the value of K is plus or minus 4
they have equal roots .
compare the above equation with ax^2+bx+c=0
a=1. b=2√k. c=8
b^2 - 4ac = 0
Here, b = - k√3, a = 3, c = 4
Given equation is 3x^2 - k√3x + 4 = 0
Now, b^2 - 4ac = 0
(- k√3)^2 - 4(3)(4) = 0
3k^2 - 48 = 0
k^2 = 48 ÷ 3
k^2 = 16
k = ± 4
^2-k root3x+4+9 has equal roots....