CBSE BOARD X, asked by Normal0Student, 1 year ago

Show that the quadratic equation 4x^2 + 12x + 15 has no real zeroes

Answers

Answered by sanya55
6
Heya!!Here is your answer friend ⤵⤵

an \: equation \: has \: no \: real \: roots \: when \\  \sqrt{b {}^{2} - 4c }   < 0 \\ here \\  \sqrt{b {}^{2} - 4ac }  =  \sqrt{12 {}^{2} - 4 \times 4 \times 15 }  \\  =  \sqrt{144 - 4 \times 60}  \\  \sqrt{144 - 240}  =  \sqrt{ - 96}
This value is less than zero. Hence it has no real roots



Hope it helps you ✌✌

sanya55: use middle term splitting then
sanya55: but this one is easy as well as quick
sanya55: and BTW this question is from Quadratic Equation only
Normal0Student: idk why this was given in my polynomial worksheet
sanya55: I don't know
sanya55: but this question is from Quadratic Equation
sanya55: for sure
sanya55: anyways you can try by Middle term Splitting
Normal0Student: ok thanks
sanya55: wlcm
Answered by devbindu29
0

Answer:

Heya!!Here is your answer friend ⤵⤵

\begin{gathered}an \: equation \: has \: no \: real \: roots \: when \\ \sqrt{b {}^{2} - 4c } < 0 \\ here \\ \sqrt{b {}^{2} - 4ac } = \sqrt{12 {}^{2} - 4 \times 4 \times 15 } \\ = \sqrt{144 - 4 \times 60} \\ \sqrt{144 - 240} = \sqrt{ - 96} \end{gathered}

anequationhasnorealrootswhen

b

2

−4c

<0

here

b

2

−4ac

=

12

2

−4×4×15

=

144−4×60

144−240

=

−96

This value is less than zero. Hence it has no real roots

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