Question

If one zero of the quadratic polynomial tx2−37x+6t⁢x2-37⁢x+6 is the reciprocal of the other, then find the value of tt.​

Answer 1

SOLUTION

GIVEN

One zero of the quadratic polynomial 

$\sf{ t {x}^{2} - 37x + 6\: }$

is the reciprocal of the other

TO DETERMINE

The value of t

EVALUATION

The given Quadratic polynomial is

$\sf{ t {x}^{2} - 37x + 6\: }$

So the product of the zeroes of the polynomial

$\displaystyle \sf{ = \frac{6}{t} \: }$

Now it is given that , one zero of the quadratic polynomial is the reciprocal of the other

So the product of the zeroes of the polynomial = 1

$\therefore \displaystyle \sf{ \: \frac{6}{t} = 1\: }$

$\implies \displaystyle \sf{ t= 6\: }$

FINAL ANSWER

The required value of t is 6

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The quadratic polynomial

where α=5+2√6 and αβ=1 is

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