If sin theta and cos theta are the roots of t | vedclass

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

Question

(B) Given that $\sin 	heta$ and $\cos 	heta$ are the roots of the quadratic equation $ax^2 - bx + c = 0$. From the properties of roots, the sum of r

Vedclass · Accepted Answer

$a^2 - b^2 + 2ac = 0$

Vedclass · Answer

(B) Given that $\sin 	heta$ and $\cos 	heta$ are the roots of the quadratic equation $ax^2 - bx + c = 0$. From the properties of roots, the sum of roots is $\sin 	heta + \cos 	heta = \frac{b}{a}$ and the product of roots is $\sin 	heta \cdot \cos 	heta = \frac{c}{a}$. Squaring the sum of roots, we get $(\sin 	heta + \cos 	heta)^2 = (\frac{b}{a})^2$. $\sin^2 	heta + \cos^2 	heta + 2 \sin 	heta \cos 	heta = \frac{b^2}{a^2}$. Since $\sin^2 	heta + \cos^2 	heta = 1$, we have $1 + 2(\frac{c}{a}) = \frac{b^2}{a^2}$. Multiplying by $a^2$, we get $a^2 + 2ac = b^2$. Rearranging the terms, we obtain $a^2 - b^2 + 2ac = 0$.

If $\sin \theta$ and $\cos \theta$ are the roots of the equation $ax^2 - bx + c = 0$, then $a, b$ and $c$ satisfy the relation:

Similar Questions

If $2$ and $6$ are the roots of the equation $ax^2 + bx + 1 = 0$,then the quadratic equation,whose roots are $\frac{1}{2a + b}$ and $\frac{1}{6a + b}$,is:

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda)x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

If $-1$ is a twice repeated root of the equation $ax^3+bx^2+cx+1=0$,then

If $\alpha, \beta, \gamma$ are the roots of the equation $3x^3 - 9x^2 + 5x - 7 = 0$,then what is the value of $\alpha + \beta + \gamma$?

If the ratio of the roots of $x^2 + bx + c = 0$ and $x^2 + qx + r = 0$ is the same,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module