Question

If the roots of the equation 6x2 - 13x + m = 0 are reciprocal of each other, find the
value of m.
​

Answer 1

EXPLANATION.

Roots of the quadratic equation.

⇒ 6x² - 13x + m = 0.

As we know that,

Let we assume that,

⇒ One roots be = α.

⇒ Other roots = 1/α.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ α x 1/α = m/6.

⇒ 1 = m/6.

⇒ m = 6.

                                                                                                                           

MORE INFORMATION.

Conjugate roots.

(1) = D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

${\large{\pmb{\sf{\underline{Explaination...}}}}}$

★ We have to find out the value of m is the roots of the equation 6x²-13x+m=0 are reciprocal of each other.

${\large{\pmb{\sf{\underline{Knowledge...}}}}}$

Some knowledge about Quadratic Equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ Discriminant is given by b²-4ac

• Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

★ D > 0 then roots are real and distinct.

★ D = 0 then roots are real and equal.

★ D < 0 then roots are imaginary.

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${\large{\pmb{\sf{\underline{Assumptions...}}}}}$

★ Let a be one of the root of equation.

★ Let 1/a be be one of the another root of equation (1/a because roots are reciprocal of each other #AlreadyGiven)

${\large{\pmb{\sf{\underline{Using \; formula...}}}}}$

★ Product of zeros of any quadratic equation is given by ➝

${\small{\underline{\boxed{\sf{:\implies \alpha \beta \: = c/a}}}}}$

${\large{\pmb{\sf{\underline{Solution...}}}}}$

~ To solve this question we just have to use the given formula and the assumptions.

${\small{\underline{\boxed{\sf{\leadsto Formula \: = \alpha \beta \: = c/a}}}}} \\ \\ \leadsto \sf Formula \: = \alpha \beta \: = c/a \\ \\ \leadsto \sf Here, \: c \: and \: a \: are \: m \: and \: 6 \: respectively \\ \\ \leadsto \sf a \times 1/a \: = m/6 \\ \\ \leadsto \sf a \: cancel \: a \\ \\ \leadsto \sf 1 = \: m/6 \\ \\ \leadsto \sf m \: = 6$

Henceforth, the value of m is 6.