Let [r] denote the greatest integer not excee | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given equation is $(3 + \alpha) x^2 + (6 + 2 \alpha) x + (5 + 2 \alpha) = 0$.For the roots to be complex,the discriminant $D$ must be less tha

Vedclass · Accepted Answer

$-2$

Vedclass · Answer

(A) The given equation is $(3 + \alpha) x^2 + (6 + 2 \alpha) x + (5 + 2 \alpha) = 0$.For the roots to be complex,the discriminant $D$ must be less than $0$.$D = (2 \alpha + 6)^2 - 4 (\alpha + 3) (2 \alpha + 5) $4(\alpha + 3)^2 - 4(\alpha + 3)(2 \alpha + 5) Dividing by $4$: $(\alpha + 3)(\alpha + 3 - 2 \alpha - 5) $(\alpha + 3)(-\alpha - 2)  0$.This implies $\alpha  -2$.Comparing with $\alpha > L$ or $\alpha The condition $L y^2 + M y + r For this to hold for all $y \in R$,the coefficient of $y^2$ must be negative (which is $-2 $D = (-3)^2 - 4(-2)(r) $9 + 8 r The greatest integer $[r]$ not exceeding $r$ is $[-1.125] = -2$.

Let $[r]$ denote the greatest integer not exceeding $r$. The roots of the equation $3 x^2 + 6 x + 5 + \alpha (x^2 + 2 x + 2) = 0$ are complex numbers whenever $\alpha > L$ or $\alpha < M$. If $(L - M)$ is minimum,then the greatest value of $[r]$ such that $L y^2 + M y + r < 0$ for all $y \in R$ is:

Similar Questions

If $a, b, c$ are distinct positive real numbers and $a^2+b^2+c^2=1$,then the value of $ab+bc+ca$ is

If a polynomial $P(x)$ of degree $4$ is given by $P(x) = 2x^4 + ax^3 + bx^2 + cx + d$ such that $P(1) = 4, P(2) = 7, P(3) = 12$,and $P(4) = 19$,then find the value of $P(5)$.

If the equation whose roots are $p$ times the roots of the equation $x^4-2ax^3+4bx^2+8ax+16=0$ is a reciprocal equation,then $|p|=$ :

If the quadratic equation formed by eliminating $x$ from $x^2+\alpha x+\beta=0$ and $xy+l(x+y)+m=0$ has the same roots as that of the given quadratic equation,then the set of values of $\beta$ is

Let $a, b, c$ be non-zero real numbers such that $a+b+c=0$. Let $q=a^2+b^2+c^2$ and $r=a^4+b^4+c^4$. Then,

Vedclass Test Series

Exam Paper Generator

Online Exam Module