Find the quadratic equation having one root- 3 - 2-5

The correct option is B x^2 6x 11 = 0 If one of the roots is 3 2√(5) . Then the other root will be 3 + 2√(5) Thus, sum of roots=6 ...

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Standard X

Mathematics

Applications of Second Degree Equations

Find the quad...

Question

Find the quadratic equation having one root: $3 - 2 \sqrt{5}$

x^{2} - 2 x - 11 = 0

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x^{2} - 6 x - 11 = 0

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x^{2} - 7 x - 11 = 0

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x^{2} - 3 x - 11 = 0

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Solution

The correct option is B $x^{2} - 6 x - 11 = 0$
If one of the roots is $3 - 2 \sqrt{5}$ . Then the other root will be $3 + 2 \sqrt{5}$
$T h u s, s u m o f r o o t s = 6$
$P r o d u c t o f r o o t s = (3 - 2 \sqrt{5}) (3 + 2 \sqrt{5}) = 0$
$\Rightarrow 9 + 6 \sqrt{5} - 6 \sqrt{5} - 20 = 0$
$\Rightarrow 9 - 20 = - 11$
The equation is : $x^{2} - S x + P = 0$
$x^{2} - 6 x - 11 = 0$

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Find the quadratic equation having one root: 3−2√5

The correct option is B x2−6x−11=0If one of the roots is 3−2√5. Then the other root will be 3+2√5Thus, sum of roots=6Product of roots=(3−2√5)(3+2√5)=0 ⇒9+6√5−6√5−20=0 ⇒9−20=−11The equation is : x2−Sx+P=0x2−6x−11=0

Find the quadratic equation having one root: $3 - 2 \sqrt{5}$