koli123able
Find 'p' if 3x^2+2x+3p=0 has real & different roots.
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ANSWER = p<1/9
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koli123able
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I have no idea on solving this question....
Xavier
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A quadratic has real and different roots if the descriminant is greater than zero: \[\Delta > 0\]
koli123able
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delta?? u mean discriminant?
ParthKohli
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Yes.
Xavier
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Yup
koli123able
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so how D>0 ??
Xavier
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What do you mean? Set the discriminant to be greater than zero
b^2-4ac > 0
koli123able
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I mean how is discriminant greater than zero can u explain?
harsimran_hs4
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if d > 0 then there are real and different roots
d = 0 real and equal roots
d < 0 imaginary roots
agent0smith
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Real and different...? I'm guessing you mean real and distinct. But yes you can use the discriminant. When the discriminant is less than zero, it will have complex/imaginary roots, as the quadratic formula takes the square root of the discriminant (
http://www.purplemath.com/modules/quadform.htm
)
\[3x^2+2x+3p=0 \]\[ax^2+bx+c = 0\]
so here, a=3, b = 2 and c = 3p
discriminant is \[b^2-4ac > 0 \]
koli123able
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If D>0 then sqrt(b^2-4ac) is a real number and roots are real and unequal
koli123able
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am I right?
harsimran_hs4
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\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]
try putting different values of d and check out
harsimran_hs4
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yes you are!!
koli123able
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as D>0 and D=b^2-4ac
so, (2)^2-4*3*3p>0
4-36p>0
4>36p
1/9>0
koli123able
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is this ok?
Xavier
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You lost a p at the end
koli123able
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oh sorry I typed it in hurry
koli123able
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p<1/9