Question

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Answer 1

Step-by-step explanation:

We have,

The points $A(x,2),\:\:B(-3,4)\:\:\&\:\:C(7,-5)$ are collinear.

So, area of triangle formed by these lines will be zero

So,

$\left| \begin{array}{ccc} x &2 &1 \\ - 3 &4 &1 \\ 7 & - 5 & 1\end{array} \right| = 0$

$\tt{ \red{ \: \large{ •} \: \: R _{1} \to \: R _{1} - R _{2}}}$

$\implies \left| \begin{array}{ccc} x + 3 & - 2 &0 \\ - 3 &4 &1 \\ 7 & - 5 & 1\end{array} \right| = 0$

$\tt{ \red{ \: \large{ •} \: \: R _{2} \to \: R _{2} - R _{3}}}$

$\implies \left| \begin{array}{ccc} x + 3 & - 2 &0 \\ - 10 &9 &0\\ 7 & - 5 & 1\end{array} \right| = 0$

$\tt{ \red{ \: \large{ •} \: Opening \: \: by \: \: C_{3} }}$

$\implies 1.\left| \begin{array}{ccc} x + 3 & - 2\\ - 10 &9\end{array} \right| = 0$

$\implies \: 9(x + 3) - ( - 2)( - 10) = 0$

$\implies \: 9(x + 3) - 20 = 0$

$\implies \: 9x + 27 - 20 = 0$

$\implies \: 9x + 7 = 0$

$\implies \: x = - \frac{7}{9}$

Answer 2

Answer:

5

Step-by-step explanation:

Given:-

zeroes of x²-kx+6 are in the ratio 3:2.

Asked:-

find the value of k

Solution:-

Let zeroes are 3p and 2p

then,

3p*2p = 6

6p²=6

p²=1

p=1 ...( 1 )

3p + 2p = k

5p = k

put the value of p,

5×1 = k

k=5