If a2a-p-b2b-p-c2c-p- where a- b- c- p - then value of a b-b c-c a is

The correct option is C 0Let nbsp; a^2(a+p)=b^2(b+p)=c^2(c+p)=k a^3+pa^2 k = 0 b^3+pb^2 k = 0 c^3+pc^2 k = 0 So, x^3+px^2 k = 0 has roots as a, b, c, the ...

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Standard XIII

Mathematics

Relations between Roots and Coefficients : Higher Order Equations

If a2a+p=b2b+...

Question

If $a^{2} (a + p) = b^{2} (b + p) = c^{2} (c + p),$ where $a, b, c, p \in R,$ then value of $a b + b c + c a$ is

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Solution

The correct option is C $0$
Let
$a^{2} (a + p) = b^{2} (b + p) = c^{2} (c + p) = k a^{3} + p a^{2} - k = 0 b^{3} + p b^{2} - k = 0 c^{3} + p c^{2} - k = 0$

So, $x^{3} + p x^{2} - k = 0$ has roots as $a, b, c$ , then
$a b + b c + c a = \frac{coefficient of x}{coefficient of x^{3}} ∴ a b + b c + c a = 0$

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If a2(a+p)=b2(b+p)=c2(c+p), where a,b,c,p∈R, then value of ab+bc+ca is

The correct option is C 0Let a2(a+p)=b2(b+p)=c2(c+p)=ka3+pa2−k=0b3+pb2−k=0c3+pc2−k=0 So, x3+px2−k=0 has roots as a,b,c, then ab+bc+ca=coefficient of xcoefficient of x3∴ab+bc+ca=0

If $a^{2} (a + p) = b^{2} (b + p) = c^{2} (c + p),$ where $a, b, c, p \in R,$ then value of $a b + b c + c a$ is