Find the value of a and b for which x=3/4 and x= -2 are the roots of the equation ax2+bx-6=0.
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Find the value of a and b for which x=3/4 and x= -2 are the roots of the equation ax2+bx-6=0.
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Answer:
x = 3/4
x = -2
ax2 + bx - 6 = 0
=> a*3/4^2 + b*-2 = 0
=> 3a/4^2 + -2b = 0
=> 3a/4 + -2b = √0
=> 3a + -2b = 0*4
=> 3a - 2b = 0
=> 3a = 0 + 2b
=> 3a = 2b
=> a/b = 2/3
Therefore,
a = 2. ANS.
b = 3. ans.
Verified answer
[tex] \tt{given : }[/tex]
[tex] \tt{ \dag \:x = \frac{3}{4} }[/tex]
[tex] \tt{ \dag \: x = - 2}[/tex]
the given equation is
[tex] \tt{a {x}^{2} + bx - 6 = 0 }[/tex]
so..we have to fill the values of x in the equation.
[tex] \tt{a( \frac{4}{3}) {}^{2} + b( \frac{4}{3} ) - 6 = 0}[/tex]
[tex] \tt{a( \frac{16}{9} ) + b( \frac{4}{3} ) - 6 = 0}[/tex]
[tex] \tt{ \frac{16a}{9} + \frac{4b}{3} - 6 = 0}[/tex]
[tex] \tt{ \frac{16a}{9} + \frac{4b - 18}{3} = 0}[/tex]
LCM is equalled to 9
[tex] \tt{\frac{16a}{9} \times 9 + \frac{4b - 18}{3} \times 9 = 0 }[/tex]
[tex] \tt{ \frac{16a + 3(4b - 18)}{9} = 0 }[/tex]
[tex] \tt{16a + 12b - 54 = 0}[/tex]
Divide whole equation by 2
[tex] \tt{8a + 6b - 27 = 0}[/tex]