Question

please answer this x^2+3x-6=0

Answer 1

Given :-

${x}^{2} + 3x - 6 = 0$

To find = Roots of the equation?

Solution :-

${x}^{2} + 3x - 6 = 0$

Now compare this equation with the standard equation of quadratic equation

$a {x}^{2} + bx + c = 0$

Hence

$a = 1 \\ b = 3 \\ c = (- 6)$

Now apply Shreedharacharya's formula

$x = \frac{b± \sqrt{b {}^{2} - 4ac } }{2a}$

Hence,

$x = \frac{1± \sqrt{(1) {}^{2} - 4 \times 1 \times ( - 6)} }{2 \times 1}$

$x = \frac{1± \sqrt{1 + 24} }{2}$

$x = \frac{1±5}{2} = > x_1( \alpha ) = \frac{1 - 5}{2} = - 2$

$and \: \: x_2( \beta ) = \frac{1 + 5}{2} = 3 \: \: \: \: \: \: ans$

Steps to solve a quadratic equation :-

• Step 1: To use the quadratic formula, the equation must be equal to zero.

• Step 2: Identify a, b, and c and plug them into the quadratic formula.

• Step 3: Use the order of operations to simplify the quadratic formula.

• Step 4: Simplify the radical, if you can.

Answer 2

Step-by-step explanation:

Given :-

{x}^{2} + 3x - 6 = 0x2+3x−6=0

To find = Roots of the equation?

Solution :-

{x}^{2} + 3x - 6 = 0x2+3x−6=0

Now compare this equation with the standard equation of quadratic equation

\begin{gathered}a {x}^{2} + bx + c = 0 \\ \\\end{gathered}ax2+bx+c=0

Hence

\begin{gathered}a = 1 \\ b = 3 \\ c = (- 6)\end{gathered}a=1b=3c=(−6)

Now apply Shreedharacharya's formula

\begin{gathered}x = \frac{b± \sqrt{b {}^{2} - 4ac } }{2a} \\\end{gathered}x=2ab±b2−4ac

Hence,

\begin{gathered}x = \frac{1± \sqrt{(1) {}^{2} - 4 \times 1 \times ( - 6)} }{2 \times 1} \\\end{gathered}x=2×11±(1)2−4×1×(−6)

\begin{gathered}x = \frac{1± \sqrt{1 + 24} }{2} \\\end{gathered}x=21±1+24

\begin{gathered}x = \frac{1±5}{2} = > x_1( \alpha ) = \frac{1 - 5}{2} = - 2 \\\end{gathered}x=21±5=>x1(α)=21−5=−2

and \: \: x_2( \beta ) = \frac{1 + 5}{2} = 3 \: \: \: \: \: \: ansandx2(β)=21+5=3ans

Steps to solve a quadratic equation :-

Step 1: To use the quadratic formula, the equation must be equal to zero.

Step 2: Identify a, b, and c and plug them into the quadratic formula.

Step 3: Use the order of operations to simplify the quadratic formula.

Step 4: Simplify the radical, if you can.