Question

Find k if the root of the equation 2xsquare plus kx plus 3 equals to zero are equal

Answer 1

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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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Answers

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

Answer 2

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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