The expression x^2 + 2bx + c has a positive v | vedclass

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

Question

(D) The given expression is $f(x) = x^2 + 2bx + c$.By completing the square,we can write:$f(x) = (x^2 + 2bx + b^2) - b^2 + c$$f(x) = (x + b)^2 + (c -

Vedclass · Accepted Answer

$b^2 < c$

Vedclass · Answer

(D) The given expression is $f(x) = x^2 + 2bx + c$.By completing the square,we can write:$f(x) = (x^2 + 2bx + b^2) - b^2 + c$$f(x) = (x + b)^2 + (c - b^2)$Since $(x + b)^2 \ge 0$ for all real $x$,the expression $f(x)$ will always be positive if the constant term $(c - b^2)$ is strictly greater than $0$.Therefore,$c - b^2 > 0$,which implies $c > b^2$ or $b^2 < c$.

The expression $x^2 + 2bx + c$ has a positive value for all real $x$ if:

Similar Questions

The value of $k$ for which the roots $\alpha, \beta$ of the equation $x^{2}-6x+k=0$ satisfy the relation $3\alpha+2\beta=20$ is:

If the difference of the roots of $x^2 - px + 8 = 0$ is $2$,then the value of $p$ is

If $x(x-3)=-1,$ then the value of $x^{3}(x^{3}-18)$ is

The roots of the equation $x^2 + bx - c = 0$ where $b, c > 0$ are:

The roots of the equation $x^2 + ax + b = 0$ are $p$ and $q$. Then,the equation whose roots are $p^2q$ and $pq^2$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module