Find k if the root of the equation 2xsquare plus kx plus 3 equals to zero are equal
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gokulkannan8383
23.12.2017
Math
Secondary School
+13 pts
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Find the values of k for quadratic equation 2x2 + kx + 3 = 0, so that they have two equal roots.
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aravind74 Helping Hand
Given,
2x^2+Kx+3
here it is in the form ax^2+bc+C=0
here a=2, b=K, c=3
if it has two equal roots. then ∆=0
b^2-4ac=0
k^2-4(2)(3)=0
k^2-24=0
k^2=24
k=√24
k=2√6
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abhi178
abhi178 Genius
we have to find the values of k for quadratic equations 2x² + kx + 3 = 0 so that they have two equal roots.
we know, quadratic equation will be equal only when
discriminant, D = b² - 4ac = 0
on comparing 2x² + kx + 3 = 0 with general form of quadratic equation , ax² + bx + c = 0 we get, a = 2, b = k and c = 3
so Discriminant , D = (k)² - 4(2)(3) = 0
or, k² - 24 = 0
or, k = ± √24 = ±2√6
hence, the value of k = 2√6 or -2√6
Step-by-step explanation:
- Given Eqn. : 2x^2+kx+3=0
- Given roots are equal i.e., let roots be 'α' & 'β' then, α=β
- In this eqn. a=2,b=k,c=3
- Since α=β
- => { -k+√(k^2-4x2x3)}/(2x2) = { -k-√(k^2-4x2x3)}/(2x2)
- => -k+√(k^2-24) = -k-√(k^2-24)
- => √(k^2-24) +√(k^2-24)=0
- => 2√(k^2-24)=0
- => (k^2-24)= 0
- => k = √24 = 2√6
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