Question

Q1.During the time of flood in some parts of Bihar and Odisha, a group of students decided to help them with clothes, food items , medicines, etc. So, this group collected some amount of rupees from the various sources which is represented by ax⁴ + 2x³ – 3x² + bx – 4. If number of students is represented by x² – 4, then find the value of a and b. ​​

Answer 1

Step-by-step explanation:

Given:During the time of flood in some parts of Bihar and Odisha, a group of students decided to help them with clothes, food items , medicines, etc. So, this group collected some amount of rupees from the various sources which is represented by ax⁴ + 2x³ – 3x² + bx – 4. If number of students is represented by x² – 4.

To find: Find the value of a and b.

Solution:

Total students (x²-4) must be the factor of ax⁴ + 2x³ – 3x² + bx – 4.

Thus,use factor theorem

$</p><p>\begin{gathered} {x}^{2} - 4 = 0 \\ \\ (x - 2)(x + 2) = 0 \\ \\ \bold{x = 2} \\ or \\ \bold{x = - 2} \\ \end{gathered}$

1)Put x=2

$\begin{gathered}a( {2)}^{4} + 2( {2)}^{3} - 3( {2})^{2} + b(2) - 4 = 0 \\ \\ 16a + 16 - 12 + 2b - 4 = 0 \\ \\ 16a + 2b = 0 \\ \\ or \\ \\ \bold{8a + b = 0} \: \: \: ...eq1\\ \end{gathered}$

2) Put x=-2

$\begin{gathered}a( { - 2)}^{4} + 2( { - 2)}^{3} - 3( { - 2})^{2} + b( - 2) - 4 = 0 \\ \\ 16a - 16 - 12 - 2b - 4 = 0 \\ \\ 16a - 2b = 32 \\ \\ or \\ \\ \bold{8a - b = 16} \: \: \: ...eq2\\\end{gathered}$

Solve eq1 and eq2,Add both

$\begin{gathered}8a+b=0\\8a-b=16\\----------\\16a=16\\\bold{\green{a=1}}\\\end{gathered}$

put value of a in eq1

$\begin{gathered}8a + b = 0\\\\8\times 1+b=0\\\\\bold{\red{b=-8}}\\\end{gathered}$

Final answer:

Value of a and b are 1 and -8 respectively.

Hope it helps you.

To learn more on brainly:

When the polynomial 2x³ + 3x² + 3x – a is divided by x² – 1, the remainder is 5x + b, then the value of under root a+b+6...

https://brainly.in/question/43553649

Answer 2

Answer:

Q1.During the time of flood in some parts of Bihar and Odisha, a group of students decided to help them with clothes, food items , medicines, etc. So, this group collected some amount of rupees from the various sources which is represented by ax⁴ + 2x³ – 3x² + bx – 4. If number of students is represented by x² – 4, then find the value of a and b.