The root of the quadratic equation x-2-5x-alpha-1-alpha-6-0 where alpha is the constant are-1- -8203-alpha-1- alpha-6- -8203-2- alpha-1- -alpha-6- -8203-3- -alpha-1- alpha-6- -8203-4- -alpha-1- -alpha-6-

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Byju's Answer

Standard XII

Mathematics

Roots of a Quadratic Equation

The root of t...

Question

The root of the quadratic equation x^2+5x-(alpha+1)(alpha+6)=0 where alpha is the constant are,
1. alpha+1, alpha+6
2. alpha+1, -(alpha+6)
3. -(alpha+1), alpha+6
4. -(alpha+1), -(alpha+6)

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Solution

$The given quadratic equation is, x^{2} + 5 x - (α + 1) (α + 6) = 0 \Rightarrow x^{2} + (α + 6) x - (α + 1) x - (α + 1) (α + 6) = 0 \Rightarrow x [x + (α + 6)] - (α + 1) [x + (α + 6)] = 0 \Rightarrow [x - (α + 1)] [x + (α + 6)] = 0 \Rightarrow x - (α + 1) = 0 or x + (α + 6) = 0 \Rightarrow x = (α + 1) or x = - (α + 6)$

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Similar questions

1, $α$ , $α^{2}$ ,............................ $α^{6}$ are the roots of the equation x = $(1)^{\frac{1}{7}}$ .Find the quadratic equation whose roots are A = $α$ + $α^{2}$ + $α^{4}$ , B = $α^{3}$ + $α^{5}$ + $α^{6}$ .

If 1, $α$ , $α^{2}$ , $α^{3}$ ,................. $α^{6}$ are the roots of the equation x = $(- 1)^{\frac{1}{7}}$ .Find the value of

$α^{4}$ + $α^{6}$ + $α^{7}$ + $α^{5}$ + $α^{7}$ + $α^{8}$ + $α^{7}$ + $α^{9}$ + $α^{10}$

Q. If

α

is a non real root of the equation

x^{6} - 1 = 0

then

\frac{α^{2} + α^{3} + α^{4} + α^{5}}{α + 1} =

Q. Prove the following identities.

2 (s i n^{6} α + c o s^{6} α) - 3 (s i n^{4} α + c o s^{4} α) + 1 = 0

Q. If

α

is the non real root of

x^{6} = 1

then

\frac{α^{5} + α^{3} + α + 1}{α^{2} + 1}

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The root of the quadratic equation x^2+5x-(alpha+1)(alpha+6)=0 where alpha is the constant are, 1. ​alpha+1, alpha+6 ​2. alpha+1, -(alpha+6) ​3. -(alpha+1), alpha+6 ​4. -(alpha+1), -(alpha+6)

The given quadratic equation is, x2 + 5x - α+1α+6 = 0⇒x2 + α+6x - α+1x - α+1α+6 = 0⇒xx + α+6 - α+1x + α+6 = 0⇒x - α+1x + α+6 = 0⇒x - α+1 = 0 or x + α+6 = 0⇒x = α+1 or x = - α+6

The root of the quadratic equation x^2+5x-(alpha+1)(alpha+6)=0 where alpha is the constant are,
1. alpha+1, alpha+6
2. alpha+1, -(alpha+6)
3. -(alpha+1), alpha+6
4. -(alpha+1), -(alpha+6)