Question

$<MARQUEE>50 marks <MARQUEE>$


X²+3x-6

$\bold{split \: \: not \: use \: quadratic \: formula}\ \textless \ br /\ \textgreater \ \ \textless \ br /\ \textgreater$

Answer 1

Answer:

there are two x values

x1=−3+√15i2

x2=−3−√15i2

Explanation:

Completing the square method:
Do this only when the numerical coefficient of x2is 1.
Start with the numerical coefficient of x which is the number 3.
Divide this number by 2 then square the result. That is

(32)2=94

Add 94 to both sides of the equation

x2+3x+94+6=0+94

the first three terms now become one group which is a PST-Perfect Square Trinomial

(x2+3x+94)+6=94

(x+32)2+6=94

(x+32)2=94−6 after transposing the 6 to the right side

(x+32)2=9−244

√(x+32)2=±√9−244

x+32=±√−154

x+32=±√−15√4

x+32=±√−152

Finally, transpose the 32 to the right side of the equation

x=−32±√−152

take note: √−15=√15⋅√−1=√15i

therefore

x=−32±√15i2

there are two x values

x1=−3+√15i2

x2=−3−√15i2



HOPE IT HELPS

Answer 2

$\bf{\red{QUESTION}}$ :- Solve equation by quadratic formula .

$\bf{Equation\:={x}^{2}+3x-6}$


$\bf{ \green{let \: us \: first \: find \: discriminant}}$

D=b^2-4ac

Here,

b=3 , a = 1 and c= -6

So,

$\bf{d = {3}^{2} - 4 \times 1 \times - 6}$


$\bf{ = 9 + 24}$


$\bf{ = 33}$


Since D > 0 , equation has positive real roots .

Roots of quadratic equation by quadratic formula=


$= \bf{ \frac{ - b + \sqrt{d} }{2a} } \: and \: \frac{ - b - \sqrt{d} }{2a}$


$= \bf \frac{ - 3 + \sqrt{33} }{2 \times 1} \: and \: \frac{ - 3 - \sqrt{33} }{2 \times 1}$


$= \bf \frac{ - 3 + 5.74 }{2} \: and \: \frac{ - 3 - 5.74}{2}$


$= \bf \frac{2.74}{2} \: and \: \frac{ - 8.74}{2}$


$= \bf{2.37 \: and \: 4.37}$



$\bf \underline \pink{ \huge{hope \: it \: helps}}$