Consider two quadratic expressions f x - ax 2- bx - c and g x - ax 2- px - q a - b - c - p - q - R - b - p such that their discriminents are equal-If f x - g x has a root x - a thenA- - will be A-M- of the roots of fx-0 and gx-0B- -will be A-M of the roots f x -0C- - will be A-M- of the roots of g x -0D- -will be A-M- of the roots of f x -0 or g x -0

The correct option is A α will be A.M. of the roots of f(x) = 0 and g(x) = 0 a^3+ba+c=a^3+pa+q = gt; α= q c/b p b^2 4ac=p^2 4aq b^2 p^2 = 4a(c q) b+p = 4a(c ...

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Byju's Answer

Standard XI

Mathematics

Geometric Progression

Consider two ...

Question

Consider two quadratic expressions f(x)= $a x^{2} + b x + c$ and g(x)= $a x^{2} + p x + q$ (a,b,c,p,q $\epsilon$ R, b≠p)such that their discriminents are equal. If f(x)=g(x) has a root x=a then.

α will be A.M of the roots f(x) = 0

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α will be A.M. of the roots of g(x) = 0

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α will be A.M. of the roots of f(x) = 0 or g(x) = 0

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α will be A.M. of the roots of f(x) = 0 and g(x) = 0

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Solution

The correct option is D
α will be A.M. of the roots of f(x) = 0 and g(x) = 0

$a^{3} + b a + c$ = $a^{3} + p a + q$ => α= $\frac{q - c}{b - p}$

$b^{2} - 4 a c$ = $p^{2} - 4 a q$

$b^{2} - p^{2}$ = 4a(c-q)

b+p = $\frac{4 a (c - q)}{b - p}$

b+p =-4aα

α= $\frac{- (b + p)}{4 a}$ which is A.M of the roots of f(x) and g(x) = 0

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Similar questions

Q. Consider two quadratic expressions

f (x) = a x^{2} + b x + c

and

g (x) = a x^{2} + p x + q

(b \neq q)

such that their discriminants are equal. If

f (x) = g (x)

has a root

x = α

, then?

Q. Let

f (x) = a x^{2} + b x + c

and

g (x) = A x^{2} + b x + λ,

where

a \neq 0, A \neq 0, a, b, c, A, λ \in R

. Roots of

f (x) = 0

and

g (x) = 0

are imaginary, then which of the following may be correct?

Q. Let

f (x) = a x^{2} + b x + c

and

g (x) = A x^{2} + b x + λ,

where

a \neq 0, A \neq 0, a, b, c, A, λ \in R

. Roots of

f (x) = 0

and

g (x) = 0

are imaginary, then which of the following may be correct?

Q. Let

f (x) = x^{2} + b_{1} x + c_{1}, g (x) = x^{2} + b_{2} x + c_{2}

. Let the real roots of

f (x) = 0

α, β

and real roots of

g (x) = 0

α + h, β + h

. The least value of

f (x)

- \frac{1}{4}

. The least value of

g (x)

occurs at

x = - \frac{7}{2}

The least value of

g (x)

Q. Assertion :Let f : R

\to

R be defined as

f (x) = a x^{2} + b x + c

, where a, b, c

ε

R and a

\neq

f (x) = 0

is having non-real roots, then

\int \frac{d x}{f (x)} = λ t a n^{- 1} (g (x)) + k

, where

λ

k

are constants and

g (x)

is linear function of

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Reason:

t a n (t a n^{- 1} g (x)) = g (x) \forall x \in R

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Consider two quadratic expressions f(x)=ax2+bx+c and g(x)=ax2+px+q (a,b,c,p,q R, b≠p)such that their discriminents are equal. If f(x)=g(x) has a root x=a then.

The correct option is D α will be A.M. of the roots of f(x) = 0 and g(x) = 0 a3+ba+c=a3+pa+q => α= q−cb−p b2−4ac=p2−4aq b2−p2 = 4a(c-q) b+p = 4a(c−q)b−p b+p =-4aα α= −(b+p)4a which is A.M of the roots of f(x) and g(x) = 0

Consider two quadratic expressions f(x)= $a x^{2} + b x + c$ and g(x)= $a x^{2} + p x + q$ (a,b,c,p,q $\epsilon$ R, b≠p)such that their discriminents are equal. If f(x)=g(x) has a root x=a then.