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 ro

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 $p$ and $q$ are non-zero real numbers and $\alpha^3 + \beta^3 = -p$,$\alpha \beta = q$,then a quadratic equation whose roots are $\frac{\alpha^2}{\beta}$ and $\frac{\beta^2}{\alpha}$ is

The values of $b$ and $c$ for which the identity $f(x+1)-f(x)=8x+3$ is satisfied,where $f(x)=bx^2+cx+d$,are

If $\alpha, \beta, 2 \beta$ are the real roots of the equation $x^3-9 x^2+k=0$ and $k \in R-\{0\}$,then $14 \beta=$

If the difference between the roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then:

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module