state whether true or false and justify your answer
. if the coefficient of x ^2 and the constant term of a quadratic equation have the same sign and the x term is zero then the quadratic equation has no real roots

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Solution

Dear student,
yes the quadratic equation will not have a real root.
Let the equation be
ax²+c=0
where a and c are positive .
then D= (b²-4ac) will be eqaul to -4ac and since both a and c are positve
D<0
hence the equation will have only imaginary solution.
Regards

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Similar questions

Question 2 (vi)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Question 2 (v)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^{2}$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

Write whether the following statemensst are true or false .Justify your answers :

1.Every quadratic equation has at least one real root

2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots .

3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots .

4.A quadratic equation with integeral coeffecient has integral roots.

Q. If the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has ________ roots.

Q. (1)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(i)

x^{2} - 3 x + 4 = 0

(2)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(ii)

2 x^{2} + x - 1 = 0

(3)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iii)

2 x^{2} - 6 x + \frac{9}{2} = 0

(4)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iv)

3 x^{2} - 4 x + 1 = 0

(5)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(v)

(x + 4)^{2} - 8 x = 0

(6)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vi)

(x - \sqrt{2})^{2} - 2 (x + 1) = 0

(7)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vii)

\sqrt{2} x^{2} - \frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0

(8)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(viii)

x (1 - x) - 2 = 0

(9)
State whether the following quadratic equation have two distinct real roots. Justify your answer
(ix)

(x - 1) (x + 2) + 2 = 0

(10)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x)

(x + 1) (x - 2) + x = 0

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state whether true or false and justify your answer . if the coefficient of x ^2 and the constant term of a quadratic equation have the same sign and the x term is zero then the quadratic equation has no real roots

Dear student, yes the quadratic equation will not have a real root. Let the equation be ax2+c=0 where a and c are positive . then D= (b2-4ac) will be eqaul to -4ac and since both a and c are positve D<0 hence the equation will have only imaginary solution. Regards

state whether true or false and justify your answer
. if the coefficient of x ^2 and the constant term of a quadratic equation have the same sign and the x term is zero then the quadratic equation has no real roots

Dear student,
yes the quadratic equation will not have a real root.
Let the equation be
ax²+c=0
where a and c are positive .
then D= (b²-4ac) will be eqaul to -4ac and since both a and c are positve
D<0
hence the equation will have only imaginary solution.
Regards