For any quadratic polynomial fx-x2-bax-ca- a 0-if - - are the roots of fx-0 andk1- k2 be two numbers such that - k1- k2- then select the correct statement-

Given: nbsp;f(x)=x^2+bax+ca; a 0 Roots of f(x)=0 are α, β and k_1, k_2 are two numbers such that: α lt; k_1, k_2 lt;β which can be shown as: Now, from t ...

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Byju's Answer

Standard XII

Mathematics

Location of Roots when Compared to two constants 'k1' & 'k2'

For any quadr...

Question

For any quadratic polynomial $f (x) = x^{2} + \frac{b}{a} x + \frac{c}{a}; a \neq 0,$
if $α, β$ are the roots of $f (x) = 0$ and
$k_{1}, k_{2}$ be two numbers such that $α < k_{1}, k_{2} < β,$ then select the correct statement.

f (k_{1}) < 0

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f (k_{1}) f (k_{2}) > 0

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f (k_{2}) < 0

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D > 0

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Solution

The correct option is D $D > 0$
Given: $f (x) = x^{2} + \frac{b}{a} x + \frac{c}{a}; a \neq 0$
Roots of $f (x) = 0$ are $α, β$ and
$k_{1}, k_{2}$ are two numbers such that: $α < k_{1}, k_{2} < β$ which can be shown as:

Now, from the graph we can find some conditions, that are:
$(i .) D > 0$
$(i i .) f (k_{1}) < 0 and f (k_{2}) < 0 \Rightarrow f (k_{1}) . f (k_{2}) > 0$

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Similar questions

Q. If

α, β

are the two roots of the quadratic polynomial

f (x) = x^{2} + \frac{b}{a} x + \frac{c}{a}; a \neq 0.

And if exactly one of the roots lies between

k_{1}, k_{2} .

Then select the correct statements where

α, β \neq k_{1}, k_{2}

Q. If

k_{1}

and

k_{2}

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Q. For any quadratic expression

f (x) = a x^{2} + b x + c; a < 0

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and if

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then select the correct statement(s).

Q. If

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k (x^{2} - x) + x + 5 = 0

. If

k_{1} & k_{2}

are the two values of k for which the roots

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are connected by the relation

(α / β) + (β / α) = 4 / 5

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For any quadratic polynomial f(x)=x2+bax+ca;a≠0, if α,β are the roots of f(x)=0 and k1,k2 be two numbers such that α<k1,k2<β, then select the correct statement.

The correct option is D D>0Given: f(x)=x2+bax+ca;a≠0 Roots of f(x)=0 are α,β and k1,k2 are two numbers such that: α<k1,k2<β which can be shown as: Now, from the graph we can find some conditions, that are: (i.) D>0 (ii.) f(k1)<0 and f(k2)<0⇒f(k1).f(k2)>0

For any quadratic polynomial $f (x) = x^{2} + \frac{b}{a} x + \frac{c}{a}; a \neq 0,$
if $α, β$ are the roots of $f (x) = 0$ and
$k_{1}, k_{2}$ be two numbers such that $α < k_{1}, k_{2} < β,$ then select the correct statement.