Note: This is the Solution of review exercise 4.4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 4.4
Question # 01: Find the square root of the following polynomials by factorization method:
\((i)\) \(\quad\) \( x^2-8x+16\)
\((ii)\) \(\quad\) \(9x^2+12x+4\)
\((iii)\) \(\quad\) \(36a^2+84a+49 \)
\((iv)\) \(\quad \)\(64y^2-32y+4 \)
\((v)\) \(\quad \) \(200t^2-120t+18\)
\((vi)\) \(\quad \) \(40x^2+120x+90\)
Question 2: Find the square root of the following polynomials by division method:
\((i)\) \(\quad\) \( 4x^4-28x^3+37x^2+42x+9\)
\((ii)\) \(\quad\) \(121x^4-198x^3-183x^2+216x+144\)
\((iii)\) \(\quad\) \(x^4-10x^3y+27x^2y^2-10xy^3+y^4 \)
\((iv)\) \(\quad \)\(4x^4-12x^3+37x^2-42x+49 \)
Question 3: An investor’s return \(\small{R(x)}\) in rupees after investing \(\small{x}\) thousand rupees is given by quadratic expression:
Factorize the expression and find the investment levels that result in zero return.
Question 4: A company’s profit \(\small{P(x)}\) in rupees from selling \(\small{x}\) units of a product is modeled by the cubic expression:
\[P(x)=-x^3-15x^2+75x-125\]
Find the break-even point(s), where the profit is zero.
Question 5: The potential energy \(\small{V(x)}\) in an electric field varies as cubic function of distance \(\small{x}\), given by:
\[V(x)=2x^3-6x^2+4x\]
Determine where the potential energy is zero.
Question 6: In structural engineering, the deflection \(\small{Y(x)}\) of a beam is given by:
\[Y(x)=2x^2-8x+6\]