Question

One root of the quadratic equation kx2 - 10x + 3 = 0
1
is
Complete the following activity, to find the
3
С
th
value of k.
2.
1r
is a root of the given quadratic equation.
H
1
Substitute x =1/3 in the given quadratic equation.

Answer 1

Given : One root of the quadratic equation kx² - 10x + 3 is 1/3.

To Find : Value of k.

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Here, we'll find the value of k by putting the value of first zero in the equation.

$\: \: \: \:$

By putting the value of (x = 1/3) in the equation, we get,

$\: \: \:$

$\sf : \implies \: k {x}^{2} - 10x + 3 = 0 \\ \\ \\\sf : \implies \:k\left( \frac{1}{3} \right) {}^{2} - 10\left( \frac{1}{3} \right) + 3 = 0 \\ \\ \\ \sf : \implies \: \frac{k}{9} - \frac{10}{3} + 3 = 0 \\ \\ \\ \sf : \implies \: \frac{k - 30 + 9}{9} = 0 \\ \\ \\ \sf : \implies \: \frac{k - 21}{9} = 0 \\ \\ \\ \sf : \implies \:k - 21 = 0 \\ \\ \\ \sf : \implies \: \underline{\boxed{\mathfrak\purple{k = 21}}} \: \bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: value \: of \: k \: is \: \bold{21}.}}$