Math, asked by AkBlaze, 7 months ago

3xsquare-2x-5-10 = 0​ find roots is roots are real​

Answers

Answered by dilipreddy80
0

Answer:

3 -2-15=0

-2/3-5=0

(-2.591) (+1927)~0

~2.5941 ~-1.9274

~ 2.5941

Answered by ishigoel02
1

Step-by-step explanation:

3x²-2x-15=0

Nature of the roots can be determined by discriminant

For the roots to be real D>=0

i.e, b²-4ac>=0

here b= -2

a= 3

c= -15

therefore. (-2)²-4(3)(-15)>=0

4+180>=0

184>=0

Since discriminant is greater than zero, two distinct roots exist.

the two roots can be found by

 \frac{ - b  +  \sqrt{ {b}^{2} - 4ac } }{2a}   \:  \: and \:  \:  \: \frac{ - b   -  \sqrt{ {b}^{2} - 4ac } }{2a}

therefore they are

 \frac{ - ( - 2) +  \sqrt{184} }{6}  \:  \: and \:  \:  \frac{ - ( - 2)  -   \sqrt{184} }{6}

on simplifying we get,

 \frac{ 2 +  \sqrt{184} }{6}  \:  \: and \:  \:  \frac{ 2  -   \sqrt{184} }{6}

 \frac{ 2 + 2 \sqrt{46} }{6}  \:  \: and \:  \:  \frac{ 2  -  2 \sqrt{46} }{6}

 \frac{ 1 + 1 \sqrt{46} }{3}  \:  \: and \:  \:  \frac{ 1  -  1 \sqrt{46} }{3} \: are \: the \: final \: simplified \: roots

Hope this helps you!!!

Please mark it as brainliest if it did help!!!

Thanks

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