If the roots of the equation x^2 - 5x + 16 = | vedclass

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

Question

(B) Given the equation $x^2 - 5x + 16 = 0$ with roots $\alpha$ and $\beta$,we have:$\alpha + \beta = 5$ and $\alpha \beta = 16$.The roots of the equat

Vedclass · Accepted Answer

$p = -1, q = -56$

Vedclass · Answer

(B) Given the equation $x^2 - 5x + 16 = 0$ with roots $\alpha$ and $\beta$,we have:$\alpha + \beta = 5$ and $\alpha \beta = 16$.The roots of the equation $x^2 + px + q = 0$ are $\alpha^2 + \beta^2$ and $\frac{\alpha \beta}{2}$.First,calculate the sum of the roots:$(\alpha^2 + \beta^2) + \frac{\alpha \beta}{2} = -p$Since $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha \beta = 5^2 - 2(16) = 25 - 32 = -7$,$-7 + \frac{16}{2} = -p \Rightarrow -7 + 8 = -p \Rightarrow 1 = -p \Rightarrow p = -1$.Next,calculate the product of the roots:$(\alpha^2 + \beta^2) \cdot \frac{\alpha \beta}{2} = q$$(-7) \cdot \frac{16}{2} = q \Rightarrow -7 \cdot 8 = q \Rightarrow q = -56$.Thus,$p = -1$ and $q = -56$.

If the roots of the equation $x^2 - 5x + 16 = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2 + \beta^2$ and $\frac{\alpha \beta}{2}$,then:

Similar Questions

If one of the roots of the equations $x^2 + ax + b = 0$ and $x^2 + bx + a = 0$ is coincident,then the numerical value of $(a + b)$ is

The product of the roots of the equation $9x^{2}-18|x|+5=0$ is

Solve the given two equations and select the correct answer from the given options.
$I.$ $35x^{2} - 53x + 20 = 0$
$II.$ $56y^{2} - 97y + 42 = 0$

For the quadratic equation $2x^2 - (p + 1)x + (p - 1) = 0$,if $\alpha - \beta = \alpha \beta$,then what is the value of $p$?

Solve the given two equations and select the correct answer from the given options:
$I.$ $679 x^{2} - 168 x^{2} = 3066$
$II.$ $\sqrt{144} y^{3} - 9 y^{3} = 1536$

Vedclass Test Series

Exam Paper Generator

Online Exam Module