Page 37 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

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(ix) If a, b are the roots of 7x2 - 5x + 3 = 0, then the sum of Version 1.1

the roots is ________.

(x) If a, b are the roots of 5x2 + 3x - 9 = 0, then product of

the roots is ________.

(xi) For a quadratic equation ax2 + bx + c = 0, 1 is equal
ab

to ________.

(xii) Cube roots of unity are ________.

(xiii) Under usual notation sum of the cube roots of

unity is ________.

(xiv) If 1, w, w2 are the cube roots of unity, then w-7 is equal

to ________.

(xv) If a, b are the roots of the quadratic equation, then the

quadratic equation is written as ________.

(xvi) If 2 w and 2 w2 are the roots of an equation, then equation

is ________.

SUMMARY

• Discriminant of the quadratic expression ax2 + bx + c is
“b2 - 4ac”.

• The cube roots of unity are
• Complex cube roots of unity are w and w2.
• Properties of cube roots of unity.

(a)The product of three cube roots of unity is one. i.e., (1) (w) (w2)
= w3 = 1
(b) Each of the complex cube roots of unity is reciprocal of the
other.
(c) Each of the complex cube roots of unity is the square of the
other.
(d) The sum of all the cube roots of unity is zero, i.e.,
1 + w + w2 = 0
• The roots of the quadratic equation ax2 + bx + c = 0 , a m 0 are

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