If $\alpha,\ \beta$ are zeroes of $x^2-6x+k$, what is the value of $k$ if $3\alpha+2\beta=20$?

Tutorialspoint

Simply Easy Learning

---

Updated on 10-Oct-2022 10:42:45

0 Views

Print Article

• Related Articles
• If $\alpha$ and $\beta$ are zeroes of $p( x)=kx^2+4x+4$, such that $\alpha^2+\beta^2=24$, find $k$.
• If $\alpha,\ \beta$ are the roots of $x^2-px+q=0$, find the value of: $( i). \alpha^2+\beta^2\ ( ii). \alpha^3+\beta^3$.
• If $\alpha,\ \beta$ are the zeroes of $f( x)=px^2-2x+3p$ and $\alpha +\beta=\alpha\beta$, then find the value of $p$.
• If $\alpha$ and $\beta$ are zeroes of $x^2-4x+1$, then find the value of $\frac{1}{\alpha}+\frac{1}{\beta}-\alpha\beta$.
• Polynomial \( f(x)=x^{2}-5 x+k \) has zeroes \( \alpha \) and \( \beta \) such that \( \alpha-\beta=1 . \) Find the value of \( 4 k \).
• If $\alpha$ and $\beta$ are the zeroes of the polynomial $ax^2+bx+c$, find the value of $\alpha^2+\beta^2$.
• Find $\alpha$ and $\beta$, if $x + 1$ and $x + 2$ are factors of $x^3 + 3x^2 - 2 \alpha x + \beta$.
• if $\alpha$ and $\beta$ are zeroes of polynomial $x^{2}-2x-15$, then form a quadratic polynomial whose zeroes are $2\alpha$ and $2\beta$.
• If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$, then find the quadratic equation whose roots are $\alpha$ and $\beta$.
• If $\alpha ,\ \beta$ are the zeroes of a polynomial, such that $\alpha+\beta=6$ and $\alpha\beta=4$, then write the polynomial.
• If $\alpha$ and $\beta$ are the zeroes of a polynomial such that $\alpha+\beta=-6$ and $\alpha\beta=5$, then find the polynomial.
• If $\alpha$ and $\beta$ are zeroes of a quadratic polynomial $4x^{2}+4x+1=0$, then form a quadratic polynomial whose zeroes are $2\alpha$ and $2\beta$.
• If \( \cos (\alpha+\beta)=0 \), then \( \sin (\alpha-\beta) \) can be reduced to(A) \( \cos \beta \)(B) \( \cos 2 \beta \)(C) \( \sin \alpha \)(D) \( \sin 2 \alpha \)
• If $\alpha$ and $\beta$ are the zeroes of the polynomial $f(x)=x^2−px+q$, then write the polynomial having $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ as its zeroes.
• Given $sin\alpha=\frac{\sqrt{3}}{2}$ and $cos\beta=0$, then find the value of $( \beta-\alpha)$.