Advertisements
Advertisements
प्रश्न
Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.
Advertisements
उत्तर
(K + 2)x2 – Kx + 6 = 0 …(1)
Substitute x = 3 in equation (1)
(–4 + 2)x2 –(–4)x + 6 = 0
⇒ –2x2 + 4x + 6 = 0
⇒ x2 – 2x – 3 = 0 ...(Dividing by 2)
⇒ x2 – 3x + x – 3 = 0
⇒ x(x – 3) + 1(x – 3) = 0
(x + 1)(x – 3) = 0
So, the roots are x = –1 and x = 3
Thus, the other root of the equation is x = –1.
APPEARS IN
संबंधित प्रश्न
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; show that : `a = (n - q)/(m - p)`
Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
Which of the following is a factor of (x – 2)2 – (x2 – 4)?
