Find $a$ for which one root is positive and other root is negative for $- x^{2} - (3 a - 2) x + a^{2} + 1 = 0$

R - 0

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ϕ

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None of the above

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R

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Solution

The correct option is D $R$
Since one root is negative and other is positive, it means one root is less than $0$ and other is greater than $0$ .
Using $a . f (d) < 0$ where $d = 0,$
$\begin{matrix} we get f (0) < 0 \Rightarrow - (a^{2} + 1) < 0 which is true for all real values of a. \Rightarrow a \in R \end{matrix}$

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Similar questions

(i) Find the value of k for which x=1 is a root of the equation $x^{2} + k x + 3 = 0$ . Also, find the other root.
(ii) Find the values of a and b for which $x = \frac{3}{4}$ and x=-2 are the roots of the equations $a x^{2} + b x - 6 = 0$ .

Q. (i) Find the value of k for which x = 1 is a root of the equation

x^{2} + k x + 3 = 0

. Also, find the other root.
(ii) Find the values of a and b for which

x = \frac{3}{4} and x = - 2

are the roots of the equation

a x^{2} + b x - 6 = 0 .

Q. Find

a

for which one root is positive and other root is negative for

- x^{2} - (3 a - 2) x + a^{2} + 1 = 0

Q. Find a for which one root is positive and other root is negative for

- x^{2} - (3 a - 2) x + a^{2} + 1 = 0

Q. The number of integral values of

a

for which

x^{2} - (a - 1) x + 3 = 0

has both roots positive and

x^{2} + 3 x + 6 - a = 0

has both roots negative is

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Find a for which one root is positive and other root is negative for −x2−(3a−2)x+a2+1=0

The correct option is D RSince one root is negative and other is positive, it means one root is less than 0 and other is greater than 0. Using a.f(d)<0 where d=0, we get f(0)<0⇒−(a2+1)<0which is true for all real values of a.⇒a∈R

Find $a$ for which one root is positive and other root is negative for $- x^{2} - (3 a - 2) x + a^{2} + 1 = 0$