marathi sentence for ghar dokyavar ghane .
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Answer:
† Question :-
The quadratic equation 2x²– 8x + p = 0 has two distinct real roots. What is the highest possible integer value of p ?
\large \dag† Answer :-
\begin{gathered}\red\dashrightarrow\underline{\underline{\sf \green{Highest \: Possible \: Integer }} }\ \\ \green{\underline{\underline{\sf Value \: of \: p \: is \: 7 }}} \\\end{gathered}
⇢
Highest Possible Integer
Valueofpis7
\large \dag† Step by step Explanation :-
We Know that If the roots are real & unequal of any quadratic equation ax² + bx + c then its discriminant is greater than zero i.e.
\begin{gathered}\large \bf \red\bigstar \: \: \orange{ \underbrace{ \underline{ \blue{b^2-4ac > 0 }}}} \\ \end{gathered}
★
b
2
−4ac>0
Here We Have,
2x²– 8x + p = 0 has two distinct real roots
Therefore,
\begin{gathered} :\longmapsto \rm {( - 8)}^{2} - 4 \times 2 \times p > 0 \\ \end{gathered}
:⟼(−8)
2
−4×2×p>0
\begin{gathered}:\longmapsto \rm 64 - 8p > 0 \\ \end{gathered}
:⟼64−8p>0
\begin{gathered}:\longmapsto \rm 8p < 64 \\ \end{gathered}
:⟼8p<64
\begin{gathered}:\longmapsto \rm p < \cancel \frac{64}{8} \\ \end{gathered}
:⟼p<
8
64
\large \red{:\longmapsto} \green{ \underline{ \overline{ \pmb{ \boxed{ \rm p < 8}}}}}:⟼
p<8
p<8
So largest possible integer value of p less than 8 will be 7 .
Therefore,
\large\purple\leadsto\large\underline{\pink{\underline{\frak{\pmb{\text Answer \: is \: 7 }}}}}⇝
Answeris7
Answeris7
\large \dag† Additional Information :-
❒ Quadratic Polynomial with one Variable :
✪ The general form of the equation is ax² + bx + c = 0.
Note :
◆ If a = 0, then the equation becomes to a linear equation.
◆ If b = 0, then the roots of the equation becomes equal but opposite in sign.
◆ If c = 0, then one of the roots is zero. ]
❒ Nature Of Roots :
✪ b² - 4ac is the discriminant of the equation.
Then,
● If b² - 4ac = 0, then the roots are real & equal.
● If b² - 4ac > 0, then the roots are real & unequal.
● If b² - 4ac < 0, then the roots are imaginary
Answer:
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