Lf - - are the roots of the equation x2-px-q-0 and -3- -3 are the roots of x2-ax-b-0- then the relation between the coefficients is

The correct option is A p^3=a+3pq nbsp;As per the given data α nbsp;+β nbsp;=p, α nbsp;β nbsp;=q and α ^ 3 +β ^ 3 =a ⇒ (α n ...

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Byju's Answer

Standard VII

Mathematics

Angle between Two Lines

lf α, β are...

Question

lf $α, β$ are the roots of the equation $x^{2} - p x + q = 0$ and $α^{3}, β^{3}$ are the roots of $x^{2} - a x + b = 0$ , then the relation between the coefficients is

p^{3} = a + 3 p q

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p^{3} = 3 a - 3 p q

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p^{3} = 3 a + 4 p q

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p = a + 3 p q

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Solution

The correct option is A $p^{3} = a + 3 p q$
$A s p e r t h e g i v e n d a t a α + β = p, α β = q a n d α^{3} + β^{3} = a \Rightarrow (α + β)^{3} - 3 α β (α + β) = a \Rightarrow p^{3} - 3 q p = a \Rightarrow p^{3} = a + 3 p q A n s w e r - O p t i o n A$

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Similar questions

Question 59 (b)

What should be added to $3 p q + 5 p^{2} q^{2} + p^{3}$ to get $p^{3} + 2 p^{2} q^{2} + 4 p q ?$

Q. If

α, a n d β

are the roots of

x^{2} + p x + q = 0

, the quadratic equation having roots

α^{3}, β^{3}

is given by

Q. Let p and q be real numbers such that

p \neq 0

p^{3} \neq 2 q

and

p^{3} \neq - q

. If

α

and

β

are non zero complex numbers satisfying

α + β = - p

and

α^{3} + β^{3} = q,

then a quadratic equation having

\frac{α}{β}

and

\frac{β}{α}

as its roots is

Q. the equation x2 +px+q=0 has roots alpha and beta.show that alpha3+beta3=3pq-q3.suppose that one root is the square of the other,then by considering ( alpha - beta2)(beta-alpha2)=0,show that q2 +q +p3-3pq=0.

Q. Let

p

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q

be real numbers such that

p \neq 0, p^{3} \neq q

and

p^{3} \neq - q

. If

α

and

β

are nonzero complex numbers satisfying

α + β = - p

and

α^{3} + β^{3} = q

, then a quadratic equation having

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and

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as its roots is -

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lf α, β are the roots of the equation x2−px+q=0 and α3, β3 are the roots of x2−ax+b=0, then the relation between the coefficients is

The correct option is A p3=a+3pqAsperthegivendataα+β=p,αβ=qandα3+β3=a⇒(α+β)3−3αβ(α+β)=a⇒p3−3qp=a⇒p3=a+3pqAnswer−OptionA

lf $α, β$ are the roots of the equation $x^{2} - p x + q = 0$ and $α^{3}, β^{3}$ are the roots of $x^{2} - a x + b = 0$ , then the relation between the coefficients is

The correct option is A $p^{3} = a + 3 p q$
$A s p e r t h e g i v e n d a t a α + β = p, α β = q a n d α^{3} + β^{3} = a \Rightarrow (α + β)^{3} - 3 α β (α + β) = a \Rightarrow p^{3} - 3 q p = a \Rightarrow p^{3} = a + 3 p q A n s w e r - O p t i o n A$