TN Maths, 12th Chapter 3 Important Questions
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Subject : Maths
Chapter : 3
Chapter : Theory Of Equations
IMPORTANT QUESTIONS
2 & 3 Marks Questions
1. Construct a cubic equation with roots.
i) 1,2 and 3
ii) 1,1 and -2
iii) 2, 1/2 and 1
2. Find a poly . equation with integer co efficient with √( √2/ √3) as a root
3. If x²+2(k + 2) x + 9k =0 has equal roots, find K.
4. Find a poly equation of minimum degree with rational coefficients having
i) 2 + √3 i
ii) 2i + 3 as a root.
5. Solve the equation
i) x⁴–9x²+20 =0
ii) x⁴– 14x²+45 =0.
6. Solve the equation 7x³– 43x²= 43x-7.
7. Discuss the nature of the roots of the following polynomial.
i) x²⁰¹⁸+1947x¹⁹⁵⁰+ 15x⁸+26x⁶+2019
ii)x⁵–19x⁴+2x³+5x²+11
8. If p and q are the roots of the equation lx²+nx+n=0. Show that √(p/q) + √(q/p) + √(n/l) =0
9. If p and q are the roots of the equation lx2+p1x+q1=0 have a common root , show that it must be equal to (pq¹ –p¹q)/(q–q1) or (q-q1)/(p1 –p)
10. If k is real , discuss the nature of the roots of the poly equation 2x²+kx +k = 0 in terms of k.
11. If p is real , discuss the nature of the roots of the roots of the equation 4x² + 4px + p + 2 =0 in terms of p.
5 Mark Questions
1. Solve the equations 6x⁴–35x³+62x²-35x+6=0
2. Find all real numbers satisfying 4^x3(2^x+²)+25=0.
3. Solve the equation 6x⁴–5x³–38x²–5x+6=0 if is known that 1/3 is a solution.
4. Show that the poly. 9x⁹+2x⁵-x⁴-7x²+2 has atleast six imaginary solutions.
5. Show that the poly x⁹-5x⁵+4x⁴+2x²+1=0 has atleast six imaginary solutions.
6. Determine the number of positive and negative roots of the equation x⁹-5x⁸-14x⁷=0.
7. Find the exact number of real zeros and imaginary of the polynomial x⁹+9x⁷+7x⁵+5x³+3x.
8. Find a polynomial equation of minimum degree with rational coefficients having √5 - √3 as a root.
9. If 2+i and 3-√2 are the roots of the equation.
X⁶-13x⁵+62x⁴-126x³+65x²+127x-140 =0
10. Find all zeros of the poly x⁶-3x⁵-5x⁴+22x³-39x+135. If it is known that 1+2i and √3 are two of its zeros.
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