Find the value of 'k' if 2x²+3x +k=0 have both real roots
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9 / 8.
Correct QuestioN :
2x² - 3x + k = 0. is a Equation and their both roots are equal so, find the value of k ?
SolutioN :
We have, Equation.
\tt \dagger \: \: \: \: \: 2 {x}^{2} - 3x + k = 0.†2x
2
−3x+k=0.
Compare With General Equation.
\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c= 0.†ax
2
+bx+c=0.
Where as,
a = 2.
b = - 3.
c = k.
→ D = b² - 4ac.
→ D = ( - 3 )² - 4( 2 )( k )
→ D = 9 - 8k.
- Both roots are Equal.
→ D = 0.
→ 0 = 9 - 8k.
→ 9 = 8k.
→ k = 9 / 8.
So, Our Quadratic Equation become,
→ 2x² - 3x + 9 / 8 = 0.
Therefore, the value of k is 9 / 8.
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Answer:
We have, Equation.
2x² + 3x + k = 0
Compare With General Equation.
ax² + bx + c = 0
Whereas,
a = 2.
b = - 3.
c = k.
→ D = b² - 4ac.
→ D = ( - 3 )² - 4( 2 )( k )
→ D = 9 - 8k.
- Both roots are Equal.
→ D = 0.
→ 0 = 9 - 8k.
→ 9 = 8k.
→ k = 9 / 8.
So, Our Quadratic Equation become,
→ 2x² - 3x + 9 / 8 = 0.
Therefore, the value of k is 9 / 8.